Chapter 9 Algebra Worksheet With Answers - Montville Township Public Schools Page 6
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31The 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 ≤
Study Guide and Review - Chapter 9
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.
The maximum value is 16.
The rocket will be in the air for a total of 2 seconds. It will go from the ground to a maximum height of 16 feet,
c.
and then it will return to the ground. Therefore, a reasonable domain for this situation is D = {t | 0 ≤ t ≤ 2} and a
reasonable range is R = {h | 0 ≤ h ≤ 16}.
Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest
tenth.
2
16. x
− 3x − 4 = 0
SOLUTION:
2
Graph the related function f (x) = x
− 3x − 4.
The x-intercepts of the graph appear to be at –1 and 4, so the solutions are –1 and 4.
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Page 6
CHECK: Check each solution in the original equation.
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