## 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.

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?

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

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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