Quadratic Area Applications

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation 
s(t) = –16t² + 64t + 80.
What will be the object's maximum height? 

• 2 ft

• 80 ft

• 144 ft

• 64 ft

A fountain shoots water in an arc over a lake that can be modeled by the graph of the equation y= -0.4x² + 8x where x is the horizontal distance (in feet) from the fountain base and y is the height (in feet) above the river.  How high does the water go?

• It goes 11.78 feet high

• It goes 20 feet high

• It goes 40 feet high

• It goes 10 feet high

A raft is dropped from a helicopter 256 feet in the air above the ocean.  Its approximate height, h, after t seconds is given by the function h(t) = -16t² + 256.  How many seconds did it take the raft to hit the water? 

• -4

• 2

• 4

• 8

A ball is thrown vertically into the air. Its height in feet after t seconds is given by the equation h(t) = –5t² + 20t. How many feet into the air will the ball be at 3 seconds?

Mathematical Equivalence

OFF

If the graph shows price vs profit, what is the maximum profit? 

• 35

• 12,000

• 12,500

• 60

The area of a certain rhombus is given by the equation L² - 5L = 6 where l represents the length of the rhombus in centimeters. What is the length of the rhombus?

• 6 cm

• -6 cm

• 1 cm

• -1 cm

If the graph shows price vs profit, at which prices would you "break even" (neither lose or gain money)? 

• 10 and 60 

• 20 and 50 

• 30 and 40 

• 35

The area of a playground is 504 square yards.  The length of the playground is (x +8) and the width is (x – 2).  Find the length and width.

• 20

• -26 and 20

• 18 and 28

• 14 and 36

Determine whether the situation described is linear, quadratic or exponential. Then, write the equation that models the situation. The area of a rectangle with a length that is three inches less than twice its width, w.

This is a _______________ function.

• Linear

• Exponential

• Quadratic