Worksheet : Transformations of Quadratic Functions

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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 Understanding
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