precalculus a unit circle approach 3rd edition ratti test bank
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Precalculus A Unit Circle Approach 3rd Edition Ratti TEST BANK
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Precalculus A Unit Circle Approach 3rd Edition Ratti SOLUTIONS
MANUAL
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the quadratic function to the correct graph.
1) y = (x + 6)2
A)
B)
10
y
10
8
8
6
6
4
2
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
C)
y
2
4
6
8 10 x
2
4
6
8 10 x
D)
10
10
8
8
6
6
4
2
4
2
-10 -8 -6 -4 -2-2
-4
Answer: A
y
2
4
6
8 10 x
-10 -8 -6 -4 -2-2
-4
-6
-6
-8
-10
-8
-10
y
2) y = -(x + 5)2 + 4
A)
B)
10
y
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
C)
y
2
4
6
8 10 x
2
4
6
8 10 x
D)
10
8
10
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
-4
-6
Answer: C
y
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-6
-8
-8
-10
-10
y
3) y = 2(x + 3)2 - 3
A)
B)
10
y
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
C)
y
2
4
6
8 10 x
2
4
6
8 10 x
D)
10
8
10
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
-4
-6
Answer: D
y
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-6
-8
-8
-10
-10
y
4) y = x2 - 7
A)
B)
10
y
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
C)
y
2
4
6
8 10 x
2
4
6
8 10 x
D)
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
Answer: C
y
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-10
-8
-10
y
5) y =
1
(x - 5)2 + 4
3
A)
B)
10
y
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2-2
2
4
6
8 10 x
-10 -8 -6 -4 -2-2
-4
-4
-6
-6
-8
-8
-10
-10
C)
y
2
4
6
8 10 x
2
4
6
8 10 x
D)
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
-4
-6
Answer: D
y
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-6
-8
-8
-10
-10
y
6) y = -
1
(x + 5)2 - 3
3
A)
B)
10
y
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2-2
2
4
6
8 10 x
-10 -8 -6 -4 -2-2
-4
-4
-6
-6
-8
-8
-10
-10
C)
y
2
4
6
8 10 x
2
4
6
8 10 x
D)
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
Answer: B
y
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
y
7) y = (x - 1)2
A)
B)
10
y
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2-2
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
C)
y
2
4
6
8 10 x
2
4
6
8 10 x
D)
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
Answer: C
y
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
y
8) y = -(x + 6)2 + 5
A)
B)
10
y
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
C)
y
2
4
6
8 10 x
2
4
6
8 10 x
D)
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
-4
-6
Answer: B
y
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-6
-8
-8
-10
-10
y
9) y = 2(x - 4)2 - 3
A)
B)
10
y
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
y
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
C)
2
4
6
8 10 x
2
4
6
8 10 x
D)
10
y
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-10
-8
-10
y
Answer: B
Find the quadratic function y = f(x) that has the given vertex and whose graph passes through the given point.
10) (4, 96)
1
A) y = 4x2
B) y = 6x2
C) y = x2
D) y = -6x2
6
Answer: B
11) (-4, -96)
A) y = -6x2
B) y = -
1 2
x
6
C) y = -4x2
D) y = 6x2
1 2
x
3
D) y = 3x2
Answer: A
12) (3, 3)
A) y = -
1 2
x
3
B) y = - 3x2
C) y =
Answer: C
13) vertex: (4, 1) passing through: (3, 2)
A) y = x2 - 4x + 1
B) y = - x2 - 8x + 1
C) y = x2 - 8x + 17
D) y = 3x2 - 8x + 17
C) y = - x2 + 4x + 2
D) y = x2 + 4x + 2
Answer: C
14) vertex: (-2, -2) passing through: (-4, 2)
A) y = x2 + 2x + 2
B) y = -4x2 - 4x - 2
Answer: D
15) vertex: (-1, -4) passing through: (-3, -8)
A) y = -3x2 + 2x + 5
B) y = -x2 + 1x - 4
C) y = x2 + 2x - 4
D) y = -x2 - 2x - 5
Answer: D
16) vertex (8, 6); passing through (4, 7)
1
A) y = (x + 8)2 - 6
B) y = (x - 8)2 + 6
16
C) y =
1
(x + 8)2 + 6
16
D) y =
1
(x - 8)2 + 6
16
Answer: D
17) vertex (0, 8); passing through (-2, 0)
A) y = 8x2 + 8
B) y = -2x2 - 8
C) y = -2x2 + 8
D) y = x2 + 8
C) y = -5(x - 5)2
D) y = -5(x + 5)2
Answer: C
18) vertex (-5, 0); passing through (-6, -5)
A) y = (x - 5)2
B) y = (x + 5)2
Answer: D
19) vertex (-4, -7); passing through (5, -1)
A) y = 6(x - 4)2 - 7
B) y =
2
(x + 4)2 + 7
27
C) y =
8
(x - 4)2 + 7
81
D) y =
2
(x + 4)2 - 7
27
Answer: D
20) vertex
4 4
4 2
, ; passing through - ,
3 3
15 15
A) y = C) y =
15
4 2 4
x32
3
3
B) y = -
4 2 4
1 5
x3
3
3 2
D) y =
15
4 2 4
x+
32
3
3
4 2 4
15
+
x+
32
3
3
Answer: B
21) vertex
4
8
11
,; passing through
, -1
3
9
9
8
A) y = -9(x + a)2 9
Answer: B
8
B) y = -9(x - a)2 9
8
C) y = -9(x - a)2 +
9
8
D) y = -9(x + a)2 +
9
The graph of a quadratic function is given. Find the standard form of the function
22)
y
5
4
3
2
1
-3
-2
-1
1
2
3
4
5
6
7 x
-1
-2
-3
-4
-5
A) f(x) = (x + 2)2 - 1
B) f(x) = -(x - 2)2 - 1
C) f(x) = (x - 2)2 + 1
D) f(x) = (x - 2)2 - 1
C) f(x) = -(x + 4)2 + 1
D) f(x) = -(x - 4)2 + 1
Answer: D
23)
5
y
4
3
2
1
-7
-6
-5
-4
-3
-2
-1
1
2
3 x
-1
-2
-3
-4
-5
A) f(x) = -(x + 4)2 - 1
Answer: C
B) f(x) = (x + 4)2 + 1
24)
y
1
-7
-6
-5
-4
-3
-2
-1
1
2
3 x
-1
-2
-3
-4
-5
-6
-7
-8
-9
A) f(x) = -(x + 2)2 + 3
B) f(x) = -(x + 2)2 - 3
C) f(x) = -(x - 2)2 - 3
Answer: B
25)
2
y
1
-3
-2
-1
1
2
3
4
5
6
7 x
-1
-2
-3
-4
-5
-6
-7
-8
A) f(x) = -
1
(x + 4)2 - 3
2
C) f(x) = -2(x - 4)2 - 3
Answer: C
B) f(x) = -(x - 4)2 - 3
D) f(x) = -
1
(x - 4)2 - 3
2
D) f(x) = (x + 2)2 - 3
26)
y
5
4
3
2
1
-2
-1
1
2
3
4
5
6
8 x
7
-1
-2
-3
-4
-5
A) f(x) =
1
(x - 4)2 - 3
2
B) f(x) =
1
(x + 4)2 - 3
2
C) f(x) = 2(x - 4)2 - 3
D) f(x) = (x - 4)2 - 3
Answer: A
Graph the function by starting with the graph of y = x 2 and using transformations.
27) f(x) = (x - 1)2
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
5
-5
-5
-10
-10
10
x
C)
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
5
10
x
5
10
x
Answer: A
28) f(x) = 4(x - 1)2 - 4
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
5
10
x
5
10
x
Answer: B
29) f(x) = -5(x + 2)2 + 1
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
5
-5
-5
-10
-10
10
x
10
x
Answer: B
30) f(x) = (x - 3)2 - 4
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
y
10
-10
10
10
-10
x
-10
-10
C)
D)
y
y
10
10
-10
10
x
-10
-10
10
x
-10
Answer: B
Write the quadratic function in the standard form y = a(x - h)2 + k.
31) y = x2 - 18x
A) y = (x - 18)2 - 324
B) y = (x - 9)2 - 81
C) y = (x + 9)2 - 9
D) y = (x + 18)2 - 18
B) y = (x - 3)2 + 10
C) y = (x + 3)2 - 10
D) y = (x + 3)2 + 10
B) y = -2(x + 4)2 + 5
C) y = (x + 4)2 + 5
D) y = 2(x + 4)2 + 5
Answer: B
32) y = x2 + 6x - 1
A) y = (x - 3)2 - 10
Answer: C
33) y = -2x2 - 16x - 27
A) y = -2(x - 4)2 + 5
Answer: B
Graph the given function. Identify the vertex and the intercepts.
34) y = x2 + 2x - 8
y
10
5
-10
-5
5
-5
-10
10
x
A) Vertex: (1, - 9)
x-intercepts: -2 and 4
y-intercept: -8
B) Vertex: (1, - 9)
x-intercepts: -2 and 4
y-intercept: 8
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C) Vertex: (- 1, - 9)
x-intercepts: -4 and 2
y-intercept: -8
10
5
5
5
10
-10
y
5
5
-10
-5
-10
10
-5
-10
-5
35) y = 8 -x2 + 2x
-5
x
-5
Answer: C
-10
x
5
10
x
y
10
-5
10
D) Vertex: (- 1, - 9)
x-intercepts: 4 and 2
y-intercept: -8
y
-10
5
10
x
A) Vertex: (- 1, 9)
x-intercepts: -4 and 2
y-intercept: 8
B) Vertex: (1, - 9)
x-intercepts: -2 and 4
y-intercept:-8
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C) Vertex: (1, 9)
x-intercepts: -4 and 2
y-intercept: 8
10
5
5
5
10
-10
y
5
5
-10
-5
-10
10
-5
-10
-5
36) y = x2 + 5x + 6
-5
x
-5
Answer: D
-10
x
5
10
x
y
10
-5
10
D) Vertex: (1, 9)
x-intercepts: -2 and 4
y-intercept: 8
y
-10
5
10
x
A) Vertex:
1
5
,2
4
B) Vertex:
x-intercepts: -3 and -2
y-intercept: 6
1
5
,2
4
x-intercepts: 3 and 2
y-intercept: 6
y
-10
y
10
10
5
5
-5
5
10
x
-5
-5
-5
-10
-10
5
1
,2
4
C) Vertex: -
-10
D) Vertex: -
x-intercepts: -3 and -2
y-intercept: 6
5
5
5
10
-10
y
4
-8
-12
-5
-10
4
-4
-10
-5
8
-4
x
-5
37) y = - 2x + x2 + 6
-8
5
10
x
y
10
Answer: C
-12
x
x-intercepts: 3 and 2
y-intercept: 6
10
-5
12
10
5
1
,2
4
y
-10
5
8
12 x
7 25
,
2 4
A) Vertex:
B) Vertex: (1, -5)
x-intercepts: none
y-intercept: -6
x-intercepts: 1 and 6
y-intercept: 6
12
y
y
12
8
8
4
4
-12
-12
-8
-4
4
-8
-4
12 x
8
4
8
12 x
4
8
12 x
-4
-4
-8
-8
-12
-12
C) Vertex: (1, 5)
x-intercepts: none
y-intercept: 6
D) Vertex: (1, -1)
x-intercepts: 0 and 2
y-intercept: 0
y
y
-12
-8
12
12
8
8
4
4
-4
4
12 x
8
-8
-8
-12
-12
y
10
5
5
-5
-10
-4
-4
38) y = - x2 - 2x - 1
-5
-8
-4
Answer: C
-10
-12
10
x
A) Vertex: (1, 0)
x-intercept: 1
y-intercept: 1
B) Vertex: (1, 0)
x-intercept: 1
y-intercept: -1
y
y
-10
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C) Vertex: (-1, 0)
x-intercept: -1
y-intercept: -1
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
39) y = -3x2 + 24x - 50
y
10
5
-5
x
5
10
x
y
10
Answer: C
-10
10
D) Vertex: (-1, 0)
x-intercept: -1
y-intercept: 1
y
-10
5
5
10
x
-5
-10
22
A) Vertex (-4, -2)
x-intercepts: none
22
y-intercept 3
B) Vertex (-4, -2)
x-intercepts: none
y-intercept: -50
y
10
y
10
5
5
-10
-10
-5
5
10
-5
5
10
x
5
10
x
x
-5
-5
-10
-10
D) Vertex: (4, -2)
x-intercepts: none
y-intercept: -50
C) Vertex (4, -2)
x-intercepts: none
22
y-intercept: 3
y
10
y
10
5
5
-10
-10
-5
5
10
-5
x
-5
-5
-10
-10
Answer: D
40) y = -5x - 7 + 2x2
y
12
8
4
-12
-8
-4
4
8
12
x
-4
-8
-12
23
A) Vertex: -
5
81
,4
8
B) Vertex:
x-intercepts: 1 and -
7
2
5
81
,4
8
x-intercepts: -1 and
y-intercept: -7
y-intercept: -7
y
y
-12
-8
7
2
12
12
8
8
4
4
-4
4
8
x
12
-12
-8
-4
4
-4
-4
-8
-8
-12
-12
C) Vertex: 3, - 16
x-intercepts: -1 and 7
y-intercept: -7
D) Vertex:
8
12
x
8
12
x
5 81
,
4 8
x-intercepts: -1 and
y
7
2
y-intercept: 0, 7
12
y
8
12
4
8
-12
-8
-4
4
8
x
12
4
-4
-12
-8
-8
-4
4
-4
-12
-8
-12
Answer: B
Find the axis of symmetry of the given function.
41) y = x2 - 14x + 54
A) x = 0
B) x = 5
C) x = -7
D) x = 7
Answer: D
42) f(x) = - 9x + x2 + 4
9
A) x =
2
B) x =
9
4
C) x = -
Answer: A
24
9
2
D) x = 9
43) f(x) = -3x2 + 4x
A) x = - 1
1
3
B) x =
2
3
C) x = -
B) x =
5
2
C) x = 5
D) x =
B) x = -5
C) x = -4
D) x = 4
B) x = -1
C) x = 5
D) x = -5
B) x = -1
C) x = -4
D) x = 1
B) x = 1
C) x = 0
D) x = -1
D) x = -2
Answer: B
44) f(x) = 5x - 1 -x2
5
A) x = 2
5
8
Answer: B
45) y = 2x2 + 20x + 54
A) x = 5
Answer: B
46) y = 3x2 + 6x - 2
A) x = 1
Answer: B
47) y = -2x2 - 16x - 33
A) x = 4
Answer: C
48) y = 9x2 - 72x + 145
A) x = 4
Answer: A
49) f(x) = 17x - 2x2 + 7
17
A) x =
4
B) x =
17
2
C) x = -
17
4
D) x = -
17
2
D) x = -
9
8
Answer: A
50) f(x) = 5 - 2x2 + 9x
9
A) x =
8
B) x = -
9
2
C) x =
9
4
Answer: C
Determine whether there is a maximum or minimum value for the given function, and find that value.
51) f(x) = x2 - 12x + 46
A) Maximum: -10
B) Maximum: 6
C) Minimum: 0
D) Minimum: 10
Answer: D
52) f(x) = x2 + 20x + 90
A) Minimum: -10
B) Maximum: 10
C) Maximum: -10
Answer: A
25
D) Minimum: 0
