Applications of Quadratic Functions

A ball is thrown into the air with an upward velocity of 100 ft/s. Its height, h, after t seconds is given by the function
 h = -16t² + 64t + 960.
How many seconds did it take for the ball to reach its maximum height?

• 10 seconds

• 64 seconds

• 960 seconds

• 2 seconds

Alain throws a stone off a bridge into a river below. The stone's height (in meters above the water), x seconds after Alain threw it, is modeled by:

h(x)= -5x² + 10x + 15

How many seconds after being thrown will the stone hit the water?

• -1 seconds

• 1 second

• 2 seconds

• 3 seconds

Alain throws a stone off a bridge into a river below. The stone's height (in meters above the water), x seconds after Alain threw it, is modeled by:
h(x)= -5x² + 10x + 15
What is the maximum height of the stone?

• 15 meters

• 16.5 meters

• 20 meters

• 22.2 meters

The function
f(t) = -5t²+20t + 60 
models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground? 

• 4 seconds

• -2 seconds

• 6 seconds

• 9 seconds

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

The height of a ball Doreen tossed into the air can be modeled by the function h(x) = −4.9x² + 6x + 5, where x is the time elapsed in seconds, and h(x) is the height in meters. The number 5 in the function represents:

• the initial height of the ball

• the time at which the ball reaches the ground

• the time at which the ball was at its highest point

• the maximum height the ball attained when thrown in the air

Your friend passes you the ball during a soccer game. The height off the ground is modeled by the equation

h(t) = -4t² + 12t. How high did the soccer ball get?

• 1.5 ft

• 3 ft

• 15 ft

• 9 ft

The equation f(t) = -4.9t² + 50t + 2 represents the height, in meters, of a toy rocket t seconds after launch. What is the initial height of the rocket?

• 0 m

• 2 m

• 4.9 m

• 50 m

A frog jumps in the air. The movement of the frog is modeled by the equation

h(t) = -6t² + 6t

where h(t) is the frog's height at any given time, t. What is the initial height of the frog?

• 1.5 ft

• 1 ft

• 0 ft

• 2 ft

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function: p(t) = -15x² + 600x + 60 What is the maximum profit you can make from selling tickets?

• $6060

• $20

• $600

• $10,250