Transformations of y = x 2

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1 Transformations of = Parent Parabola Lesson 11-1 Learning Targets: Describe translations of the parent function f() =. Given a translation of the function f() =, write the equation of the function. SUGGESTED LEARNING STRATEGIES: Create Representations, Quickwrite, Group Presentation, Look for a Pattern, Discussion Groups 1. Graph the parent quadratic function, f() =, on the coordinate grid below. Include the points that have -values, 1, 0, 1, and. M Notes A parent function is the simplest function of a particular tpe. For eample, the parent linear function is f () =. The parent absolute value function is f () =. The points on the parent function graph that have -values, 1, 0, 1, and are ke points that can be used when graphing an quadratic function as a transformation of the parent quadratic function.. Graph f() = on the coordinate grid below. Then graph and label g() = 3 and h() = +. A transformation of a graph of a parent function is a change in the position, size, or shape of the graph. 01 College Board. All rights reserved. 3. Make use of structure. Identif and describe the transformations of the graph of f() = that result in the graphs of g() and h(). Activit 11 Transformations of = 173

2 Lesson 11-1 M Notes. Model with mathematics. Graph f() = on the coordinate grid below. Then graph and label g() = ( ) and h() = ( + 3). Translations are transformations that change the location of a graph but maintain the original shape of a graph. For this reason, the are known as rigid transformations.. Identif and describe the transformations of the graph of f() = that result in the graphs of g() and h().. Describe each function as a transformation of f() =. Then use that information to graph each function on the coordinate grid. a. a() = ( 1) b. w() = + 01 College Board. All rights reserved. 17 SpringBoard Mathematics Algebra, Unit Quadratic Functions

3 Lesson 11-1 c. d() = ( + 3) M Notes d. j() = ( 1) + Check Your Understanding 01 College Board. All rights reserved. 7. Epress regularit in repeated reasoning. The graph of each function below is a translation of the graph of f() = b k units, where k > 0. For each function, tell which direction the graph of f() is translated. a. g() = + k b. h() = ( + k) c. j() = k d. m() = ( k) 8. What is the verte of the function p() =? Justif our answer in terms of a translation of f() =. 9. What is the ais of smmetr of the function q() = ( + 1)? Justif our answer in terms of a translation of f() =.. Reason abstractl. The function r() is a translation of the function f() =. What can ou conclude about the direction in which the parabola given b r() opens? Justif our answer. If ou need help with Item 7, tr substituting a positive number for k and then graphing each function. Activit 11 Transformations of = 17

4 Lesson 11-1 M Notes 11. Each function graphed below is a translation of f() =. Describe the transformation. Then write the equation of the transformed function. a. g() b. h() c. j() 8 d. k() 8 01 College Board. All rights reserved. 17 SpringBoard Mathematics Algebra, Unit Quadratic Functions

5 Lesson Use a graphing calculator to graph each of the equations ou wrote in Item 11. Check that the graphs on the calculator match those shown in Item 11. Revise our answers to Item 11 as needed. M Notes TECHNOLOGY TIP Check Your Understanding 13. Eplain how ou determined the equation of k() in Item 11d. 1. Critique the reasoning of others. g() The graph shows a translation of f() =. A student sas that the equation of the transformed function is g() = ( ). Is the student correct? Eplain. 1. The graph of h() is a translation of the graph of f() =. If the verte of the graph of h() is ( 1, ), what is the equation of h()? Eplain our answer. When ou graph a function on a graphing calculator, the distance between tick marks on the -ais is not alwas the same as the distance between tick marks on the -ais. To make these distances the same, press ZOOM, and select : ZSquare. This step will make it easier to compare our calculator graphs to the graphs in Item College Board. All rights reserved. LESSON 11-1 PRACTICE Make sense of problems. Describe each function as a transformation of f() =. 1. g() = 17. h() = ( + ) 18. j() = ( ) k() = ( + ) Each function graphed below is a translation of f() =. Describe the transformation. Then write the equation of the transformed function m() n(). What is the verte of the function p() = ( ) +? Justif our answer in terms of a translation of f() =. 3. What is the ais of smmetr of the function q() = ( + 8)? Justif our answer in terms of a translation of f() =. Activit 11 Transformations of = 177