Quadratic Story Problems

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t² +128t  
When will the object reach its maximum height?

• 4 ft
• 0 seconds
• 0 ft
• 4 seconds

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= -15x² +600x +60 , where x is the price of each ticket.  What is the maximum profit you can make from selling tickets?

• $6060
• $20
• $600
• $10,250

Jason launched a rocket for a physics experiment. This equation can be used to find the height (h), in feet, of the rocket after t seconds. 
h = -16t² + 288t + 8
How many seconds will it take for the rocket to reach a height of 1,304 feet? 

• 9.0 seconds 
• 9.6 seconds
• 81.0 seconds
• 82.0 seconds

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

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

The height of a water balloon that is launched into the air is given by h(t) = -5x²+20x+25. When will the balloon explode on the ground?

• 5 seconds

• 1 second

• 2 seconds

• 3 seconds

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.
h = -5t² + 45 
When is the ball at ground level?

• only at t = 0 seconds 
• only at t = 3 seconds
• only at t = 9 seconds
• at both t = 0 seconds and t = 3 seconds

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t² + 90t gives the height h of the ball after t seconds.
How many seconds will it take the ball to hit the ground?

• 126.56 ft
• 5.625 sec
• 2.81 sec
• 0 ft

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air. The equation

h = -2t² + 7t + 4 models the toy's height, h, from the ground at t seconds after he threw it. How high is the toy after 1 second?

• 2

• 4

• 9

• 10

• 15