Algebra II
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5.5 Quadratic Application Problems ÿ..ÿ
1. A company knows that R = -2.5p2 + 500p models the revenue they make per month of a
certain maker of bicycles, where p represents the price and R the revenue. What price will
maximize the revenue? What is the maximum revenue?
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2. The equation for the height of a baseball kit 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?
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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) = -16tÿ ÷ 64t ÷ 50, where t is the time in
seconds. Find the maximum height above the beach that the rock will attain.
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4. A manufacturer of microwave 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: RIP) = 125P -ÿPÿ.
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What t_ri_ce 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 hi9b does the ball go? For how many seconds is the ball in the air before it hits the
ground?
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6. A model for a company's revenue is R = -15p2 + 300p + 12000 where p is the price in dollars of
the company's product. What pr,!ÿ€e will maximize revenue? Find the maxl mum revenue.
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7. The equation for the motion of a projectile fired straight up with initial velocity 64 ft/s is
h = 64t - 16t2, where h is the height in feet and t is the time in seconds. Find the time the
projectile needs to reach its highest point. How high will itgo? ........
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8. Stevie's Shirts makes a profit based onP = -200cÿ + 2400c- 4700. If P represents profit in
hundreds of dollars and c represents number of shir.ts in thousands, how many shirts will Stevie
sell to maximize his profit? What will his profit be?
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