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Algebra II
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5.5 Factoring and Square Root Method WS
1. A company knows that R = -2.5p2 + 500p models the revenue they make per month of a
certaÿ maker of bicycles, where p represents the price and R the revenue. What price will
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maximize the revenue? What is the maximum revenue.
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2. The equation for the height of a baseball hit straight up with initial velocity 32 ft/s is
h = 32t -16t2, where h is the height in feet and t is the time in seconds. How long will it be until
the baseball reaches its highest point? How high will it go? - lip tt "ÿ 1 ,ÿ'ÿ.t)
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3. The height in feet (s) of a rock thrown upward at an initial speed of 64 ft/s from a cliff 50
ft above an ocean beach is given by the function: s(t) = -16t2 + 64t + 50, where t is the time in
seconds. Find the maximum heig.ÿt above the beach that the rock will attain.
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4. A manufo
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mÿcrowave ovens believes that the revenue in dollars (R) the company
receives is related to the price in dollars (P) of an oven by the function: R(P) = 125P _1p2.
What price will give the maximum revenue?
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5. Suppose you throw a ball straight up from the ground with a velocity of 80 ft/s. As the ball
moves upward, gravity slows it. Eventually the ball begins to fall back to the ground. The height
h of the ball after t seconds in the air is given by the quadratic function h(t) = -16t2 + 80t.
How high does the ball go? For how many seconds is the ball in the air before it hits the
ground?
1. x2+6x+8=O
2. x2 +18--9x
3. 2xÿ ix=3
4. xa - lOx + 25 = 0
5. 2xa + 6x = -4
6. 3xa = 16x+12
7. 5xa = 80
8. xa-4=O
9. 2xÿ =32
10.9xa=25
13. x* - 4x = 0
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3xa=48
11. 3xÿ-15=0
14. 6xa+4x=O
17. 2xa=8x
12. 5xa - 40 = 0
15. 12xa - 147 = 0
18. 4xÿ-80=0
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