Worksheet: Transformations of Quadratic Functions Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Which correctly identifies the values of the parameters a, h, and k for the function a. c. b. d. ____ 2. What is the equation of this graph? y 2 1 2 1 1 2 3 4 5 6 7 8 x 1 2 3 4 5 6 7 8 a. c. b. d. ____ 3. Which function includes a translation of 3 units to the left? a. c. b. d. ____ 4. Which equation shows a translation of 3 left and vertical compression by a factor of 2 to the graph of ? a. c. b. d. ____ 5. Joanne hit a ball straight up into the air. The height of the ball in metres, is given by the function t seconds after the ball is hit. In how many seconds will the ball hit the ground? a. 3 c. 9 b. 6 d. 45 ____ 6. Kevin threw a ball straight up with an initial speed of 20 metres per second. The function describes the ball's height, in metres, t seconds after Kevin threw it. What are the coordinates of the vertex? a. c. (20, 2) b. d. ____ 7. Which equation describes a parabola that opens downward, is congruent to , and has its vertex at (0, 3)? a. c. b. d. ____ 8. List the sequence of steps required to graph the function a. horizontal translation 4 units to the right, vertical compression by a factor of 1, vertical translation 6 units down b. horizontal translation 4 units to the right, reflection in x-axis, vertical translation 6 units down c. horizontal translation 4 units to the left, vertical translation 6 units up, reflection in x-axis d. horizontal translation 4 units to the left, reflection in x-axis, vertical translation 6 units down ____ 9. Which function matches the graph? y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 x 1 2 3 4 5 a. c. b. d. ____ 10. Consider a parabola P that is congruent to , opens upward, and has vertex . Now find the equa- tion of a new parabola that results if P is reflected in the x-axis and translated 3 units down. a. c. b. d. ____ 11. The graphs of and another parabola are shown below. What is a possible equation for the second para- bola? y 5 4 y=? 3 2 1 y=x2 5 4 3 2 1 1 2 3 4 5 x 1 2 3 4 5 a. c. b. d. Short Answer 12. The graph of f(x) is shown below. Graph the transformed functions in the same set of axes. y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 x 1 2 3 4 5 13. Name a function to describe each graph. GRAPH A y 5 4 f(x) = ? 3 2 f(x)=x^2 1 5 4 3 2 1 1 2 3 4 5 x 1 2 3 4 5 GRAPH B y 5 4 3 f(x)=x^2 2 1 g(x)=? 5 4 3 2 1 1 2 3 4 5 x 1 2 3 4 5 14. How does the shape of the graph of compare with the graph of ? Explain. 15. The net annual income of an engineer in Barry's company can be modelled by , where x is the age of the engineer and . What is the axis of symmetry? 16. Sketch the final graph of the function , Problem 17. A parabola that opens downward has its vertex at (3, 0) and a y-intercept at (0, -9) The parabola is congruent to the parabola described by the function a) What is the equation of the function? b) Draw a graph of the function using key points. c) What is the axis of symmetry? d) What are the values of the parameters a, h, and k? Worksheet: Transformations of Quadratic Functions Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 - Graphing Quadratic Functions by Using Transformations 2. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 - Graphing Quadratic Functions by Using Transformations 3. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 - Graphing Quadratic Functions by Using Transformations 4. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 - Graphing Quadratic Functions by Using Transformations 5. ANS: B PTS: 1 REF: Application OBJ: 1.5 - Graphing Quadratic Functions by Using Transformations 6. ANS: B PTS: 1 REF: Application OBJ: 1.5 - Graphing Quadratic Functions by Using Transformations 7. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 - Graphing Quadratic Functions by Using Transformations 8. ANS: D PTS: 1 REF: Communication OBJ: 1.6 - Using Multiple Transformations to Graph Quadratic Functions 9. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: 1.6 - Using Multiple Transformations to Graph Quadratic Functions 10. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: 1.6 - Using Multiple Transformations to Graph Quadratic Functions 11. ANS: A PTS: 1 REF: Application OBJ: 1.6 - Using Multiple Transformations to Graph Quadratic Functions SHORT ANSWER 12. ANS: y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 x 1 2 3 4 5 PTS: 1 REF: Knowledge and UnderstandingDownload Link: