Quadratic Functions Review Worksheets With Answer Key Page 12

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ID: A
3. ANS:
a) The maximum profit occurs at the vertex (3.5, 4500) or $4500.
b) Substitute d = 10 into the equation:
R = −50 10 − 3.5
+ 4500
2
(
)
= −50 6.5
+ 4500
2
(
)
= −2112.50 + 4500
= 2387.5
The income would be $2387.50.
PTS: 1
DIF: Average
OBJ: Section 3.1
NAT: RF 3
TOP: Investigating Quadratic Functions in Vertex Form
KEY: vertex form | vertex
4. ANS:
a) Find the t-intercepts to determine the domain.
h = −5t
+ 4t + 1
2
= (−5t − 1)(t − 1)
1
The t-intercepts are −
and 1. Since t ≥ 0 , the domain is {t ∈ R| 0 ≤ t ≤ 1} .
5
To find the range, write the equation in vertex form.
h = −5t
+ 4t + 1
2
= −5(t
− 0.8t) + 1
2
= −5(t
− 0.8t + 0.16 − 0.16) + 1
2
= −5(t − 0.4)
+ 0.8 + 1
2
= −5(t − 0.4)
+ 1.8
2
The parabola opens downward, so the maximum value is the h-coordinate of the vertex, or 1.8. Thus, the
range is {h(t) ∈ R| 0 ≤ h(t) ≤ 1.8}
b) The initial height of the ball is the h-intercept, or 1 m.
c) The time it takes for the ball to hit the ground is the t-intercept that is greater than zero, or 1 s.
PTS: 1
DIF: Easy
OBJ: Section 3.2
NAT: RF 4
TOP: Investigating Quadratic Functions in Standard Form
KEY: domain | range | intercept
5

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