Quadratic Real World Problems

A ball is thrown into the air with an initial velocity of 18 m/s. The height of the ball can be modeled by the equation h(t) = -2.5t^2 + 18t + 4, where h(t) represents the height of the ball at time t in seconds. How long does it take for the ball to reach its maximum height?

• 2.5

• 4.2

• 3.6

• 6.8

A diver is standing on a platform above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Use the formula: h(t) = −16 t² + 8t + 24

How high is the platform?

• .25 ft

• 24 ft

• 25 ft

• 8 ft

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

When would you reach 16 feet above the water?

• 8 seconds

• 1 second

• 1/2 second

• 1/4 second

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t² +84t + 100 models the height, h, of the fireworks at any given time, t. How high do the fireworks get?

• 2.625

• 6.25

• 100

• 200

• 210.25

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

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

You are snowboarding on a mountain at Breckenridge 23 ft up in the air. You are about to go off a jump. At 0 seconds, your standing up on the mountain up at 23 ft, then you begin to go off your jump. After one second, you are 37 ft above the ground. After 2 seconds, you are at 47 feet. After three seconds, you are at 53 feet. After four seconds, you reach your maximum height of 55 feet.

Select the equation that matches this situation.

What is the shape of this graph? Does it open up or down? Select all that apply.

• Up

• Down

• V-Shape

• U-Shape

The graph below shows the height, in feet, over time, in seconds, of a student's rocket. Use the graph to answer the questions below. What was the maximum height the rocket reached?

• 25 feet

• 45 feet

• 65 feet

• 85 feet

• 3 seconds

• 46 seconds

• 5 seconds

• 10 seconds