Chapter 9 Algebra Worksheet With Answers - Montville Township Public Schools Page 3
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31The minimum value is 0.
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
≥ 0}.
2
12. y = −x
+ 3x
SOLUTION:
2
a. For y = −x
+ 3x, a = –1, b = 3, 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 = 1.5.
The maximum value is 2.25.
c. The domain is all real numbers. The range is all real numbers less than or equal to the minimum value, or {y|y ≤
2.25}.
2
13. y = x
− 2x − 3
SOLUTION:
2
a. For y = x
− 2x − 3, a = 1, b = –2, and c = –3. Because a is positive, the graph opens upward, so the function has
a minimum value.
b. The minimum 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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The minimum value is –4.
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