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Points reflected over an axis graphically Graph functions using reflections about the x-axis and the

• Graph functions using reflections about the x-axis and the y-axis Another transformation that can be applied to a function is a reflection over the x - or y -axis. A vertical reflection reflects a graph vertically across the x -axis, while a horizontal reflection reflects a graph horizontally across the y -axis
• You see, the graph of - f (x) is the graph of f (x) reflected over the x -axis. In math, we call - f (x) a reflection of f (x) over the x -axis, and we would call - f (x) and f (x) reflecting..
• A point and its reflection over the line x=-1 have two properties: their y-coordinates are equal, and the average of their x-coordinates is -1 (so the sum of their x-coordinates is -1*2=-2). So (2,3) reflected over the line x=-1 gives (-2-2,3) = (-4,3). (1 vote
• The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. For example, when point P with coordinates (5,4) is reflecting across the X axis and mapped onto point P', the coordinates of P' are (5,-4)
• In standard reflections, we reflect over a line, like the y-axis or the x-axis. For a point reflection, we actually reflect over a specific point, usually that point is the origin. $\text {Formula} \\ r_ { (origin)} \\ (a,b) \rightarrow (\red -a, \red -b)$ Example
• utes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique features make Virtual Nerd a viable alternative to private tutoring
• Point reflection, also called as an inversion in a point is defined as an isometry of Euclidean space. It can also be defined as the inversion through a point or the central inversion. Use our online point reflection calculator to know the point reflection for the given coordinates

Reflection over the x-axis A reflection over the x-axis can be seen in the picture below in which point A is reflected to its image A'. The general rule for a reflection over the x-axis: (A, B) → (A, − B Given a point and a definition of a horizontal or vertical reflection, plot the reflection on a coordinate plane or identify the coordinates of the reflected point When the point (3,-5) is reflected over the x-axis, which number changes and what does it change to? (3, 5) Determine the ordered pair for (3, -5) when it has been reflected over the x-axis

Graphically, this is the same as reflecting over the -axis. We're just going to treat it like we are doing reflecting over the -axis. Let's see how far away it is. Point is units from the line , so we're going units to the right of it. Keep the same height. And we have . Same thing for points and It's point above the -axis so we'll go point below the -axis. So, . And just connect the points. Then we can see our reflection over the -axis. When we reflect over the -axis, something happens to the coordinates. The initial coordinates change. The coordinate stays the same but the coordinate is the same number but now it's negative When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (its sign is changed). If you forget the rules for reflections when graphing, simply fold your paper along the x-axis (the line of reflection) to see where the new figure will be located We can also reflect the graph of a function over the x-axis (y = 0), the y-axis(x = 0), or the line y = x. Making the output negative reflects the graph over the x -axis, or the line y = 0 . Here are the graphs of y = f ( x ) and y = - f ( x )

������ Learn how to reflect points and a figure over a line of symmetry. Sometimes the line of symmetry will be a random line or it can be represented by the x. A reflection across x-axis is nothing but folding or flipping an object over the x axis. The original object is called the pre-image, and the reflection is called the image. If the pre-image is labeled as ABC, then t he image is labeled using a prime symbol, such as A'B'C'. An object and its reflection have the same shape and size, but the figures face in opposite directions Graph a triangle (ABC) and reflect it over the x-axis to create triangle A'B'C'. Describe the transformation. Draw a line segment from point A to the reflecting line.

Graphing Reflecting Functions - Math Class  Study

a two dimensional surface on which points are plotted and located by their x and y coordinates. It includes an origin and four quadrants The objects appear as if they are mirror reflections, with right and left reversed. When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed). Reflection in the line x = 0 i.e., in the y-axis. The line x = 0 means the y-axis Now to reflect in the y-axis. Blue graph: f(x) = x 3 − 3x 2 + x − 2. Reflection in y-axis (green): f(−x) = −x 3 − 3x 2 − x − 2. Even and Odd Functions. We really should mention even and odd functions before leaving this topic. For each of my examples above, the reflections in either the x- or y-axis produced a graph that was.

D To reflect a graph over the line y = x, switch the x and y coordinates of each point on the graph. For this graph, Point V (-2,1) becomes (1,-2) and point Z (0,1) becomes (1,0). Eliminate any graph that does not include these three points. Note that point X (-1,-1) remains the same. You can also visualize the reflection by drawing the line y. Q. A point P has coordinates (-8, -2). What are its new coordinates after reflecting point P across the x-axis A graph is labeled as Marathon Training. The horizontal axis is labeled as Weeks and the vertical axis is labeled as Time Algebra2 A triangle has points A (1, 2), B (1, 6), and C (3, 6) and is reflected over the x-axis and then over the line y = x The graph of f(x) = is reflected over the y-axis. Use the graphing calculator to graph this reflection. Which list contains three points that lie on the graph of the reflection

Reflecting points in the coordinate plane (video) Khan

Below we will see a graph showing how this all looks when full parabolas are drawn. Realize that when a = 1 we have our reference parabola:. y = (1)x 2 = x 2. When a = -1, we have:. y = (-1)x 2 = -x 2. When a = -1, all the points on the reference parabola have been reflected over the x-axis.The graph below has the reference parabola drawn in transparent light gray, and it's reflection across. The graph of f(x) is reflected across the x-axis. Write a function g(x) to describe the new graph. g(x)= Get the answers you need, now! natalierojas1977 natalierojas1977 When we have a point (x, y) and we reflect it over the x-axis, the end result of the reflection is the point (x, -y

-5) is reflected over the x-axis. What are the coordinates of corresponding points on the graph of the reflection? 4. A graph containing the points L(2, 3) & M(-4, - 6) is reflected over the y-axis. What are the coordinates of the corresponding points on the graph of the reflection? Sample Answers to Discussion Questions: 1. Reflecting over the. If the graph of f(x)= 3^x is reflected over the x-axis, what is the equation of the new graph? - 2045607

Reflection Over The X and Y Axis: The Complete Guide

• us out the front). Now for f (− x
• reflected across the x-axis, shifted left 1 unit and shifted down 3 units We should always take care of the stretching or shrinking and reflections first. Start by graphing y 2x by plotting at least 3 points. Then reflect that graph over the x -axis. Finally, take the last graph and shift 1 unit le ft and 3 units down to complete the graph. f x.
• 4. To reflect a point in the x-axis, the x-coordinate remains the same and the y-coordinate is negated. 5. To reflect a point in the y-axis, the y-coordinate remains the same and the x-coordinate is negated. 6. Graph (4,5) on the grid below. Then reflect it in the x-axis. What are the coordinates of the reflection? (4,-5) 7
• The graph of y = -f (x) can be obtained by reflecting the graph of y = f (x) over the x-axis. It can be done by using the rule given below. That is, if each point of the pre-image is (x, y), then each point of the image after reflection over x-axis will b
• In this lesson you will learn how to reflect points over the x and y axes by using a coordinate plane. Create your free account Teacher Student. Create a new teacher account for LearnZillion. All fields are required. Name. Email address. Email confirmation. Password. Password should be 6 characters or more.

Using the selection tool, select each of the three points. Under display on the menu, choose label points. Double click the Y axis. This indicates to GPS that you are about to mirror your image over the Y axis Reflect point (14, 3) over the x axis then the y axis. (1, 3) Reflect point (-1, 3) over the y axis Reflection of a Point In these printable worksheets for grade 6 and grade 7 reflect the given point and graph the image across the axes and across x=a, y=b, where a and b are parameters. Choose the Correct Reflection This practice set tasks 6th grade and 7th grade students to identify the reflection of the given point from the given options Reflections and Rotations We can also reflect the graph of a function over the x -axis (y = 0), the y -axis (x = 0), or the line y = x. Making the output negative reflects the graph over the x -axis, or the line y = 0. Here are the graphs of y = f (x) and y = - f (x)

Video: Reflect over a Point - Mathwarehouse

7:24 point is reflected in the x axis sign of; 7:26 y coordinate changes and when a point is; 7:28 reflected in y axis sign of x coordinate; 7:31 changes that's all we need to remember; 7:33 no need to even draw the graph we can; 7:35 just use this two concepts and solve; 7:38 problems right but it's not completed in; 7:41 the next session we. How can I find the coordinates of a point reflected over a line that may not necessarily be any of the axis? Example Question: If P is a reflection (image) of point (3, -3) in the line $2y = x+1$, find the coordinates of Point P This anchor chart poster is a great tool to display in your classroom. Students will be reminded how to reflect points on the coordinate plane. This anchor chart is color coordinated to help students see the difference of reflecting a point over the x-axis versus reflecting a point over the y-axis

How Do You Use a Graph to Reflect a Figure Over the X-Axis

• Point (x,y) reflects to point (x,-y) Reflection over x-axis (line of reflection: x - axis) Reflection-flip in which image has opposite orientation Transformation- a change in position, shape or size of a geometric figur
• You have done reflections before- when graphing quadratic equations, you reflect points across the axis of symmetry to find more points. A reflection can be over any line, most often the x-axis or the y-axis. In vertex form, if a is negative, all points are reflected over the x-axis. Expansions and Contractions On the graph to the left, the.
• Reflection in a Line. A reflection over a line k (notation r k) is a transformation in which each point of the original figure (pre-image) has an image that is the same distance from the line of reflection as the original point but is on the opposite side of the line. Remember that a reflection is a flip. Under a reflection, the figure does not change size
• Reflections Over the X-Axis. So let's talk about reflections over the x-axis. If we reflect a point in the x-y plane over the x-axis, the original point and the reflected image will have the same x-coordinate, will be on the same vertical line. The y-coordinate has equal absolute values and opposite signs. So we just take the y-coordinate
• A reflection in the coordinate plane is just like a reflection in a mirror. Any point or shape can be reflected across the x-axis, the y-axis, or any other line, invisible or visible. This line, about which the object is reflected, is called the line of symmetry. Let's look at a typical ACT line of symmetry problem
• Improve your math knowledge with free questions in Reflections over the x- and y-axes: graph the image and thousands of other math skills
• The coordinates of point L′ after a reflection are (-3, -5). Without graphing, tell which axis point L was reflected across. Explain your answer. _____ Answer: Point L was reflected on the y-axis. When you reflect a point across the y-axis, the sign of the x-coordinate changes, and the sign of the y-coordinate remains the same. Question 9

What is the Reflection over X-Axis? Imagine that a point is reflecting over the X-Axis. Hence, the Y-coordinates will transform in their signs oppositely but the X-coordinates stay constant. (Image to be added soon) So, if the point of reflection is labelled as [X, Y] then the same coordinates across the X-Axis would be [X, - Y] Given a function, reflect the graph both vertically and horizontally. Multiply all outputs by -1 for a vertical reflection. The new graph is a reflection of the original graph about the x-axis. Multiply all inputs by -1 for a horizontal reflection. The new graph is a reflection of the original graph about the y-axis If the graph #y=x^3 + 5# is reflected in the x axis what is the new equation? Precalculus Functions Defined and Notation Introduction to Twelve Basic Functions. 2 Answers Gerardina C. Jun 29, 2016 #y=-x^3-5# Explanation: the points reflected in the x axis have opposite y-coordinates, or. x'=x and y'=-y. so the new equation is #-y=x^3+5# that's.

The point c(x,y) is reflected over the x axis. write a translation. the point c(x,y) is reflected over the x axis. write a translation rule to derscribe the original point and its reflection. > = the arrow Previous Post Previous Find an equation of the tangent line to the graph of y. Next Post Next A cell phone company charges \$0.28 for. answer choices Reflect across the x-axis and then rotate -90 degrees around the origin Rotate -90 degrees around the origin and then translate down. Reflect across the x-axis and then reflect across the y-axis The upper portion of the graph is then reflected over the polar axis. Next, we make a table of values, as in the table below, and then we plot the points and draw the graph. See Figure 8

Point Reflection Calculato

The point P ( -4, -5) on reflection in y-axis is mapped on P. The point P on reflection in the origin is mapped on P. Find the co-ordinates of P and P. Write down a single transformation that maps P onto P Recall from the graphical transformations section that the negative sign attached to the x indicates a reflection across the y -axis. Therefore, the graph of h (x) = e -x should look exactly like the graph of f (x) = e x, reflected across the y -axis. Examine the graphs below In this graphing puzzle, the student will: 1). plot points in the first quadrant of a coordinate plane (no fractions). 2). draw line segments. 3). reflect across the y-axis. 4). reflect across the x-axis. 5). work with powers of rational numbers. 6). perform binary operations with simple fractions

To find the reflection, we need to cross the y axis which would be x=-3. The y coordinate will be the same since we are crossing the x axis and the point will still be above the x-axis. If we reflect across the x-axis, then the x-coordinate will stay the same but the y-coordinate will change sign but have the same value 2) Graph the point (-4, -4) on scratch paper, then graph the image of the point when it is reflected over the x-axis. What is the coordinate of the image? 3) Graph the point (1, 4) on scratch paper, then graph the image of the point when it is reflected over the line x = 4. What is the coordinate of the image The highest or lowest point on the graph of an absolute value function is called the vertex of an absolute function graph. A transformationopposite of hchanges a graph's size, shape, position, or orientation. A translationis a transformation that shifts a graph horizontally and/or vertically, but does not change its size, shape, or orientation 6) Reflect the point (7, 2) over the x axis _____ 7) Reflect the point (7, 2) over the y axis _____ Other types of Reflections: 1) Coordinate Reflections in Vertical and Horizontal Lines 2) Reflection in the line y = x 3) Reflection in the line y = -x 4) Reflection in the Origin Words used to Reflect 1) Reflect over Question: (1 Point) If The Graph Of The Line Y - Mx + B Is Reflected Over The Y-axis, What Will Be The Slope And Intercepts Of The New Graph? (Your Answers Will Depend On The Parameters B And M. (a) The Slope Will Be (b) The Y-intercept Will Be Y - (c) The X-intercept Will Be X

Reflect a Point - Mathwarehouse

Determine the original image's coordinates, and write them down in (x, y) format. The x axis is always the horizontal line on a graph, while the y axis is always the vertical line on a graph. Draw a line from coordinate to coordinate to ensure that the reflected image matches the original image. Flip the y coordinates of the original imag Reflect points over the x- or y-axes on coordinate plane. o Give coordinates for points on a coordinate plane. Then give the reflected points. Find the distance between the original and new points. A link to printable coordinate grid paper is here. Additional Practice Locate Aliens (game) Stock Shelves (game) Grids (game c.When the point (-15.9, 32.8) is reflected over the x-axis and then the y-axis, the image is the point (-15.9, -32.8) d. When the point (-15.9, 32.8) is reflected over the y-axis and then the x-axis, the image is the point (-15.9, -32.8) 17. In the coordinate plane, the coordin ates of point A are ( 6 , ) . Point A is reflected over the 8 5. If the graph of a line y = b + mx is reflected across the y-axis, what are the slope and intercepts of the resulting line? If the graph of a line y = b + mx is reflected across the y-axis, what are the slope and intercepts of the resulting line? Lv 7. 6 years ago. The reflection across the y-axis of the point (x, y) is (-x, y). So leave.

Reflect points (practice) Reflections Khan Academ

If the graph of the line y=mx+b is reflected over the y-axis, what will be the slope and intercepts of the new graph? (Your answers will depend on the parameters b and m. The problem I am having here is having the x-intercept depend on b and m. Any help is appreciated The point is the maximum value on the graph. We found that the polar equation is symmetric with respect to the polar axis, but as it extends to all four quadrants, we need to plot values over the interval The upper portion of the graph is then reflected over the polar axis If a point on the reference parabola is (5, 25), then what are the x- and y-coordinates on the corresponding point on the transformed parabola? About the transformed y-coordinate: Let's see, at the reference point (5, 25) the y-coordinate is y = 25. Since a = -4, this y-coordinate is reflected across the x-axis transforming it to -25

The line segment shown is reflected over the x-axis. What are the new coordinates of point B? A) (4, 3) B) (-4, 3) C) (4, -3) D) (-4, -3) Explanation: When a line is reflected across the x-axis. The y-coordinates will change signs. Any positive y's will become negative and any negative y's will become positive We label the origin, the x- and y-axis, and all four quadrants. Together, we plot the first point, (4, 5) and label it as Point A. Students annotate the problem by boxing the words 'y-axis.' My expectation is that they always box the axis over which we're rotating, as a small way to help them not reflect over the incorrect axis - xThe axis is the line y = 0 because all points on it have y coordinate zero. x- xThe y axis is the line = 0 because all points on it have coordinate zero. Earlier in this pack you learnt that a point could be reflected in the . x or y axis. Now we are going to reflect points in lines parallel to the x or y axis Point A is located at (3, -9). The point is reflected in the x-axis. Its image is located at What is the image of point (4, -7) after the transformation Graph the Reflections over the line given 10) y=1 . Homework Answers Draw the reflections for the given shape and write the points below 3) reflect over both the x and y axis a) X. 1. The function y f(x) contains the point (2, -3). The graph of y = f(x) is stretched vertically by a factor of 3 about the r-axis, reflected over the y-axis then translated right 3 units and 2 units up

Coordinate Plane (Graphing & Reflection)- Quiz Prep

1. implement into your own code -> I don't fully understand your code but I see you have two plots. Also I don't know which of them you want to reflect, but in both cases you have x-values and y-values ((h,depth) resp. (B,C)). In case you want to reflect the first one, use my code and replace x with h and y with depth
2. When a point is reflected over the y-axis, the x-coordinate changes its sign. (2,4) becomes (-2,4) or vice versa Notice that the point and its reflection are both two units horizontally away from the y-axis
3. (Apr 29, 2021) Learning how to perform a reflection of a point, a line, or a figure across the x axis or across the y axis is an important skill www.mashupmath.com. Reflecting functions introduction Khan Academy. We can reflect the graph of y=f(x) over the x-axis by graphing y=-f(x) and over the y-axis by graphing y=f(-x). See this in.
4. g the reflection across. It can be the y-axis, or any vertical line with the equation x = constant, like x = 2, x = -16, etc. Finding the axis of symmetry, like plotting the reflections themselves, is also a simple process
5. In general, when reflecting a point across the y-axis, if the coordinate of the preimage is (x, y), then the coordinate of the reflected image is (-x, y) How to find a reflection image using the lines y = x and y = -x Reflection of a point across the line y =
6. 2. You can reflect ordered pairs the x-axis and y-axis. 3. Another term for reflection is mirror image. 4. To reflect a point in the x-axis, the x-coordinate remains the same and the y-coordinate is negated. 5. To reflect a point in the y-axis, the y-coordinate remains the same and the x-coordinate is negated. 6
7. 1. Graph and connect these points: (2,2) (3,4) (6,2) (6,4). 2. On your patty paper, trace the x-axis, the y-axis, and the trapezoid. Reflect the trapezoid across the y-axis by folding the patty paper along the y-axis. Transfer the trapezoid to the graph paper. Compare the original figure to the reflected figure, including coordinate pairs

Any point or shape can be reflected across the x-axis, the y-axis, or any other line, invisible or visible. This line, about which the object is reflected, is called the line of symmetry. Let's look at a typical ACT line of symmetry problem. To find our lines of symmetry, we must divide our figure into symmetrical halves The graph of y = f (-x) can be obtained by reflecting the graph of y = f (x) through the y-axis. It can be done by using the rule given below. That is, if each point of the pre-image is (x, y), then each point of the image after reflection over y-axis will b Without graphing, find the new coordinates of the vertices of the triangle after two reflections first over the x-axis and then over the y-axis. Graph and label each figure and its reflection over the indicated axis. Then find the coordinates of the reflected image. 13 Free graphing calculator instantly graphs your math problems

To just change the locations of points in a graph along x-axis, there is a single step involved. Consider A= (-5,-8), B= (-3,-4), C= (-8,-3), D= (-6,1) a graph which is drawn with four points, three in third quadrant ((-8,-3), (-5,-8), (-3,-4)) and one point in second quadrant (-6,1) Graph C could be y = -(x - 1)(x + 5) because it might intersect the x-axis at about (+1, 0) and (-5, 0) and when x is large (say 100), then y is negative. Graph D could be y = (x + 3)2 because it only intersects the x-axis at one point, so it must have a repeated root To plot a point, start at the origin and count along the x axis until you reach the x coordinate, count right for positive numbers, left for negative. Then count up or down the number of the y coordinate (up for positive, down for negative.

Learn About Reflection Over a Horizontal Or Vertical Lin

1. Locate a point in Quadrant IV of the coordinate plane. Label the point A, and write its ordered pair next to it. a. Reflect point A over an axis so that its image is in Quadrant III. Label the image B, and write its ordered pair next to it. Which axis did you reflect over? What is the only difference in the ordered pairs of points A and B? b a) On graph paper, graph a ABC b) Graph and state the coordinates of which images Of a ABC under the composite Transformation. Translate (x*5, y-1) and then reflect over the line y=x. Then write a rule that wou d take ABC to in one transformation 1. If the coordinates Of point P are (2.-3). ther Reflect 90 degrees then rotate 180 degree Reflections We can also reflect an exponential function over the y-axis or x-axis. To reflect the function over the y-axis, we simply multiply the base, a, by -1 after raising it to the x power to get -a x

Learn About Reflection Over an Axis Over X-Axis or Y-Axi

Just like how your image is reflected in a mirror, a graph or a flat (planar) object can be reflected in the coordinate plane. It can be reflected across the x-axis, the y-axis, or any other line, invisible or otherwise. This line, about which the object is reflected, is called the line of symmetry A point P (a, b) is reflected in the X-axis to P' (2, - 3). Write down the value of a & b. P is the image of P, when reflected on the Y-axis. Write down the co-ordinates of P when P is reflected in the line parallel to the Y-axis, such that x = 4

Reflection of Point in X-Axis - Assignment Poin

1. To graph these, simply plot the points and and join them. (Note that these values can be obtained just by substituting and into the equation. We can also substitute any other or values to find two points on the line and join them. There is no need to memorise the formulas for these points.
2. It is customary to use the Greek letter theta as the symbol for the angle. Graphing points in the form is just like graphing points in the form (x, y). Along the x-axis we will be plotting, and along the in the y-axis we will be plotting the value of. The graphs that we'll draw will use values of in radians
3. A reflection in a line produces a mirror image in which corresponding points on the original shape are always the same distance from the mirror line. The reflected image has the same size as the original figure, but with a reverse orientation. Examples of transformation geometry in the coordinate plane... Reflection over y -axis: (x, y) (- x, y

Operations on Functions: Reflections and Rotations

1. The upper portion of the graph is then reflected over the polar axis. Next, we make a table of values, as in Table $$\PageIndex{3}$$, and then we plot the points and draw the graph. See Figure $$\PageIndex{8}$$
2. • Reflects a point so the line of reflection is the _____ _____ of the segment connecting the two points. • If a point is on the line of reflection, then . • It uses the line like a mirror to reflect a point/figure. A reflection is a(n) _____. l
3. The graph of y = -x 2 represents a reflection of y = x 2, over the x-axis. That is, every function value of y = -x 2 is the negative of a function value of y = x 2. In general, g(x) = -f(x) has a graph that is the graph of f(x), reflected over the x-axis. Example 3: Sketch a graph of y = x 3 and y = -x 3 on the same axes. Solution
4. 2 unit from axis 2 units from axis (020) (rotate 180 is the same as reflection over the center) ROTATION Every rotation has an angle clockwise around the origin direction' and center point. around (2, 2) Note: Rotating a function or image 180 270 270 counter-clockwise Rotating Functions: Examples reflection over the origin 90 counter-clockwis

How to reflect a point over the x axis - YouTub

Compare the positions of points (x,f(x)) and (x , - f(x)). Select and experiment with other values of a, b and c. 3 - How can the graph of - f(x) be obtained from that of f(x)? . 5 - Why do the graph of f(x) and that of - f(x) have a common x intercepts? . More on reflections: Reflection Of Graphs In x-axis. Reflection Of Graphs Of Functions Graph the point (-2, 2). Label it E. Then graph its reflection over the x-axis. Label the reflection E2

Reflection Through X Axis - onlinemath4al

Vertical Translation: f(x) + k shifts up f(x) - k shifts down 5-8 Graphing Absolute Value Functions Write an equation for each graph. 1 4 3 2 5-8 Graphing Absolute Value Functions Reflect graph across the x-axis: f(x) flips the graphs Shifts 3 to the right Shifts 2 up Shifts 2 to the left Shifts 1 up Reflect over x-axis Shifts 3 to the left. Compare the positions of points (x,f(x)) and (x , f(-x)). Select and experiment with other values of a, b and c. 3 - Select values for a, b and c to obtain quadratic functions with graphs symmetric with respect to y-axis. Compare the two graphs and explain the reflection of the graph of f(x) in the y-axis. Why are the graphs the same Step 3) Reflect those two points over the axis of symmetry to get two more points on the right side of the axis of symmetry. Step 4) Plot all of the points found (including the vertex). Step 5) Draw a curve through all of the points to graph the parabola. Let's go through these steps in detail Jump to Top of Page Step 1

Graph a triangle (ABC) and reflect it over the x-axis to

1. Graph JKL and its image after a re! ection in the x-axis. 6. Graph JKL and its image after a re! ection in the y-axis. 7. Graph JKL and its image after a re! ection in the line y = x. 8. Graph JKL and its image after a re! ection in the line y = −x. 9. In Example 3, verify that FF— ′ is perpendicular to y = −x. Re! ecting in the Line y =
2. Graph each figure and its reflection over the indicated axis. Label and find the new coordinates of the reflected image. 1) ∆TUV with vertices T(-4,-1), U(-2,-3), an
3. 3a. Fill in the table to show how points on the graph of change after the graph is reflected over the x-axis. 3b. How do the y-coordinates of the points change after being reflected over the x-axis? 3c. How do the x-coordinates of the points change after being reflected over the x-axis? 3 EXAMPLE Original Function Transformation (-7, 1) (-4, -1.
4. So im supposed to find the equation of the reflection of the x-axis and y-axis. The original equation is f(x)=3|x+5| I know to reflect over the x axis, its f(x)= -3|x+5| I thought that to reflect over the y axis it would be f(x)=3|-x+5| but that wouldnt make sense since its absolute value so it would be the same as the original function
5. f (x) three units to the right, two units up, and reflected vertically over the x-axis. Complete the following tasks: a) 15 points: Graph f (x) on the axes below and label it. Graph g(x) on the axes below and label it. b) 10 points: Write the vertex form equation for g(x) below. ____
6. Is (-3,4) the reflection of (3,4) over the y axis? If we look the location of the point on the graph, it is located at x=3, y=4. To find the reflection, we need to cross the y axis which would be x=-3. The y coordinate will be the same since we are crossing the x axis and the point will still be above the x-axis. If we reflect across the x-axis.

Then connect the five points with a smooth curve. MAKE A TABLE using x - values close to the Axis of symmetry. STEP 1: Find the Axis of symmetry y x Graphing a Quadratic Function STEP 2: Find the vertex Substitute in x = 1 to find the y - value of the vertex. 5 -1 STEP 3: Find two other points and reflect them across the Axis of symmetry Describe how to get from the original points to the new points. Answer (a): On your graph, reflect the original triangle over the ‑axis. What are the coordinates of the vertices of the new triangle? Hint (c): The original triangle has been reflected across the -axis for you. Can you find the coordinates of this triangle's vertices A. Line segment MN was reflected over the x-axis and then reflected over the y-axis. B. Line segment MN was translated 10 units to the right and then reflected over the x-axis. C. Line segment MN was rotated szr¹ clockwise about Point N and then translated 10 units to the right. D. Line segment MN was reflected over the y

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