Chapter 9 Algebra Worksheet With Answers - Montville Township Public Schools Page 5
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31The minimum value is –4.
c. The domain is all real numbers. The range is all real numbers greater than or equal to the minimum value, or {y|y
Study Guide and Review - Chapter 9
≥ –4}.
2
14. y = −x
+ 2
SOLUTION:
2
a. For y = −x
+ 2, a = –1, b = 0, and c = 2. Because a is negative, the graph opens downward, so the function has a
maximum value.
b. The maximum value is the y-coordinate of the vertex. The x-coordinate of the vertex is
.
Substitute this value into the function to find the y -coordinate.
The x-coordinate of the vertex is x = 0.
The maximum value is 2.
c. The domain is all real numbers. The range is all real numbers less than or equal to the maximum value, or {y|y ≤
2}.
2
15. BASEBALL A toy rocket is launched with an upward velocity of 32 feet per second. The equation h = −16t
+ 32t
gives the height of the rocket t seconds after it is launched.
a. Determine whether the function has a maximum or minimum value.
b. State the maximum or minimum value.
c. State a reasonable domain and range of this situation.
SOLUTION:
2
a. For h = −16t
+ 32t, a = –16, b = 32, and c = 0. Because a is negative, the graph opens downward, so the function
has a maximum value.
b. The maximum value is the y-coordinate of the vertex. The x-coordinate of the vertex is
.
Substitute this value into the function to find the y -coordinate.
The x-coordinate of the vertex is x = 1.
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