Name: ______________________ Class: _________________ Date: _________
Review Chapters 5 and 6
Describe the transformation of f (x ) = x 2 represented by g. Then graph each function.
____
1. g (x ) = − x 2
a. The graph of g is a reflection in the
y -axis of the graph of f.
b.
The graph of g is a reflection in the
x -axis of the graph of f.
c.
The graph of g is a reflection in the
x -axis of the graph of f.
d.
The graph of g is a reflection in the
y -axis of the graph of f.
1
ID: A
Name: ______________________
ID: A
Graph the function. Label the vertex and axis of symmetry.
____
2. f (x ) = 2x 2 − 5
a.
c.
b.
d.
2
Name: ______________________
____
3. g (x ) =
ID: A
1 2
x + 2x − 3
2
a.
c.
b.
d.
4. f (x ) = (x + 3 ) + 5
2
Graph the function. Label the x-intercept(s), vertex, and axis of symmetry.
5. g (x ) = −2 (x − 5 ) (x − 1)
3
Name: ______________________
ID: A
Write an equation of the parabola in vertex form.
____
6.
a.
b.
____
d.
y = −(x + 4) 2 − 9
y = −(x − 4) 2 − 9
c.
y = −0.4 (x − 5) + 7
d.
y = −2.5 (x − 5) + 7
c.
7. passes through ÊÁË 10,−3 ˆ˜¯ and has vertex ÊÁË 5,7 ˆ˜¯
2
a. y = −2.5 (x + 5) + 7
b.
____
y = (x − 4) 2 − 9
y = (x + 4) 2 − 9
y = −0.4 (x + 5) + 7
2
2
2
8. Which of the following equations represent the parabola?
a.
y = −x 2 − 6x − 5
d.
y = − (x − 5 ) (x − 1 )
b.
y = − (x − 3 ) + 4
e.
y = − (x + 5 ) (x + 1 )
c.
y = − (x + 3 ) + 4
f.
y = x 2 − 6x − 5
2
2
4
Name: ______________________
ID: A
9. A scientist creates a parabola to predict the tide level over the next 8 hours, where x is the number of hours
after midnight and y is the height of the tide (in meters).
The function f that models the tide over time is f (x ) = −0.15(x − 1.5 ) (x − 8 ) , where 0 ≤ x ≤ 8;. What is the
highest tide?
Find the degree of the monomial.
____ 10.
1 9 5
m n
5
a. 9
b. 5
c.
d.
14
45
c.
d.
y−2
−3y + 5
Find the sum.
____ 11. (−4y + 5) + (y − 3)
a. −3y + 2
b. −5y + 8
ÁÊ
˜ˆ ÁÊ 2
˜ˆ
6
____ 12. ÁÁÁÁ −5s 2 − s − 7 ˜˜˜˜ + ÁÁÁÁ − s − 6 ˜˜˜˜
7
Ë
¯ Ë 7
¯
8
a. −5s 2 − s − 13
7
8
2
b. −5s − s − 7
7
c.
d.
4
−5s 2 − s − 7
7
4
2
−5s − s − 13
7
Find the product.
____ 13. (m − 7)(9m − 1)
a.
b.
9m2 − 64m + 7
9m2 + 7
c.
d.
5
9m2 − 63m + 7
9m2 − 64m − 7
Name: ______________________
ID: A
14. (5x − 7)(2x 2 + 3x − 1)
Factor the polynomial completely.
15. 6z 2 − 42z
16. x 2 + 2x − 63
17. y 2 − 4y + 6
____ 18. The polynomial p 2 − 10p + 25 represents the area (in square inches) of a square dinner plate. Which
expression represents the side length of the plate?
2
a. ÁÊË p − 5 ˆ˜¯ in.
c. ÁÊË p − 5˜ˆ¯ in.
2
b. ÊÁË p + 25 ˆ˜¯ in.
d. ÊÁË p + 5ˆ˜¯ in.
____ 19. Which statements are true about polynomials A and B?
A = 5y 2 + y + 3
B = −2y 2 + 2
a.
b.
c.
A + B = 3y 2 + y + 5
B is a monomial.
A − B = 7y 2 − y + 1
d.
e.
f.
The degree of B is 3.
The leading coefficient of B is − 2.
The degree of A is 2.
Choose the quadratic function in standard form whose graph satisfies the given condition(s).
____ 20. passes through (4, 0)
a. f(x) = x(x − 4)
c.
f(x) = x 2 + x + 4
d.
b.
____ 21. axis of symmetry: x = −5
a. f(x) = x 2 + 10x + 9
b.
f(x) = x 2 − 5x + 9
c.
d.
6
f(x) = x 2 + x − 3
f(x) = x 2 − 4
f(x) = x 2 − 10x − 75
f(x) = x 2 − 5x − 16
Name: ______________________
ID: A
____ 22. Which function(s) could be represented by the graph?
a.
b.
j(x) = (x − 3)(x + 1)
k(x) = −x 2 + 1
c.
d.
m(x) = −(x − 3)(x + 5)
h(x) = (x − 1) 2 − 4
23. The function h = −16t 2 + 32t + 64 gives the height h (in feet) of a projectile launched from a trebuchet after t
seconds.
a. What is the maximum height of the projectile?
b. Find and interpret the axis of symmetry.
____ 24. Simplify the difference.
(−7x − 5x 4 + 5) − (−7x 4 − 5 − 9x)
a.
b.
2x 4 + 2x + 8
−14x 4 + 10x + 10
c.
d.
−14x 4 − 10x + 10
2x 4 + 2x + 10
Write a rule for g described by the transformations of the graph of f. Then identify the vertex.
____ 25. f (x ) = x 2 ; vertical stretch by a factor of 2 and a reflection in the x-axis, followed by a translation 1 unit
right.
2
a. g (x ) = −2 (x − 1 ) ; ÊÁË 1,0 ˆ˜¯
c. g (x ) = 2x 2 − 1 ; ÊÁË 0,−1 ˆ˜¯
b.
2
g (x ) = 2 (x − 1 ) ; ÊÁË 1,0 ˆ˜¯
d.
7
1
2
g (x ) = − (x − 1) ; ÊÁË 1,0 ˆ˜¯
2
Name: ______________________
____ 26. f (x ) = 6x 2 − 5 ; horizontal shrink by a factor of
ID: A
1
and a translation 2 units down, followed by a reflection in
3
the y-axis.
a.
f (x ) = 6 (3x) − 7 ; ÊÁË 0,−7 ˆ˜¯
c.
ÊÁ 1 ˆ˜ 2
f (x ) = 6 ÁÁÁÁ x ˜˜˜˜ − 7 ; ÊÁË 0,−7 ˆ˜¯
Ë3 ¯
b.
f (x ) = 18x 2 − 7 ; ÊÁË 0,−7 ˆ˜¯
d.
f (x ) = 2x 2 − 7 ; ÊÁË 0,−7 ˆ˜¯
2
____ 27. f (x ) = (x + 5 ) − 3 ; horizontal shrink by a factor of
2
in the x-axis.
2
a. f (x ) = − (5x + 5) + 1 ; ÊÁË −1,1 ˆ˜¯
b.
2
f (x ) = − (5x + 25) − 1 ; ÊÁË −25,−1 ˆ˜¯
1
and a translation 2 units up, followed by a reflection
5
c.
2
f (x ) = − (5x + 25) + 1 ; ÊÁË −5,1 ˆ˜¯
d.
2
f (x ) = − (5x + 5) − 1 ; ÊÁË −5,−1 ˆ˜¯
28. Write a quadratic function given the following. (answers may vary for a - d)
(a) x intercepts are - 1 and 4
(b) vertex is (- 1, - 25)
(c) axis of symmetry is x = 4
(d) range: y ≤ - 5
(e) passes through the points (- 2, 0), (8, 0), and (2, - 24)
29. Using the quadratic equation y = −5x 2 − 20x − 18 ,
(a) Find the vertex.
(a) Is the vertex minimum or a maximum value?
(c) Find the y-intercept.
8
ID: A
Review Chapters 5 and 6
Answer Section
1. C
2. A
3. B
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
A
C
A, C, E
a. The highest tide is about 1.58 meters at 4:45 A.M.
C
A
A
A
14.
15.
16.
17.
18.
36 − 25m2
6z(z − 7)
(x − 7)(x + 9)
unfactorable
C
1
ID: A
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
A, E, F
A
A
A, D
a. about 80 ft
b. The vertex is (1,80). So the axis of symmetry is x = 1 . On the left side of x = 1, the height increases as
time increases. On the right side of x = 1, the height decreases as time increases.
D
A
A
A
(a) y = (x + 1)(x - 4)
(b) y = (x + 1) 2 − 25
(c) y = (x − 4) 2
(d) y = −x 2 − 5
(e) y = - 1(x + 2)(x - 8)
29. (a) (- 2, 2)
(b) maximum
(c) (0, - 18)
2
Review Chapters 5 and 6 [Answer Strip]
ID: A
B
_______
3.
A
_______
2.
A
_______
6.
C
_______
1.
C
_______
7.
A, C, E 8.
_______
Review Chapters 5 and 6 [Answer Strip]
A, D 22.
_______
ID: A
A
_______
26.
A
_______
27.
C
_______
18.
A, E, F 19.
_______
C
_______
10.
D
_______
24.
A
_______
11.
A
_______
20.
A
_______
21.
A
_______
12.
A
_______
13.
A
_______
25.