Hard Quadratic Word Problems

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.
What is the maximum height of the ball?

• 126.56 ft
• 5.625 sec
• 2.81 sec
• 90 ft

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 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

A ball is thrown straight up into the air from an initial height of 49 meters with an initial velocity of 14.7 meters per second. The height of the ball in meters, h, can be modeled by the following quadratic equation, where t is the time in seconds after the ball was thrown.

h = -4.9t² + 14.7t + 49

How long after the ball was thrown did it reach its maximum height?

• 1.5 seconds

• 2 seconds

• 2.5 seconds

• 3 seconds

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function -16t² + 40t + 10. In how many seconds does it take the ball to reach its maximum height?

• 1.25 seconds

• 1.4 seconds

• 2.5 seconds

• 2 seconds

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function -16t² + 40t + 10. What is the ball's maximum height?

• 85 ft

• 40 ft

• 35 ft

• 10 ft

If each mark on the x-axis represents one second, when did the object reach the ground?

• 2.5 seconds
• 6 seconds
• 5.5 seconds
• 5 seconds

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

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

You are trying to dunk a basketball. You need to jump 2.5 feet in the air to dunk the ball. The height that your feet are above the ground is given by the function:
h(t) = -16t² + 12t
Will you be able to dunk the basketball?

• Yes
• No
• As long as I'm wearing Air Jordans