Quadratic Functions Real World Problems

If a toy rocket is launched from the ground and its height h after t seconds is given by the function h(t) = -8t² +64t.

When will the object reach its maximum height?

• 128 ft

• 0 seconds

• 0 ft

• 4 seconds

If you jump off a cliff and your path is modeled by the function,

h(t) = -16t² + 8t + 24, where t is time in seconds, how long would it take you to reach the water?

• .25 sec

• 1 sec

• 1.5 sec

• 2 sec

A soccer ball is kicked from the ground and its path is modeled by the function h(t)= -t² + 5t, where t is time in seconds. What is the maximum height of the ball?

• 5 ft

• 6.25 ft

• 18.75 ft

• 2.5 ft

Your younger sibling is standing on his deck, which is 4 feet off the ground. They toss their toy up into the air. The toy's height, h, from the ground at t seconds after they threw it is modeled by the function h(t) = -2t² + 7t + 4. How long does it take the toy to hit the ground?

• .5 sec

• 2 sec

• 4 sec

• 8 sec

The height of a water balloon that is launched into the air is given by h(t) = -5t² + 20t + 25. When will the balloon explode on the ground?

• 5 seconds

• 1 second

• 2 seconds

• 3 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 where p is the profit and x is the number of tickets sold:

p= -15x² + 600x + 60

What is the maximum profit you can make from selling tickets?

• $6060

• $20

• $600

• $10,250

The height of a water balloon that is launched into the air is given by h(t) = -5t² + 40t + 2. From what height was the balloon released?

• 2 meters

• 5 meters

• 40 meters

• 20 meters

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

A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds. For which interval is the ball's height always decreasing?

A ball is thrown straight up at an initial velocity of 54 feet per second. The height of the ball t seconds after it is thrown is given by the formula h(t) = 54t − 12t² .

How many seconds after the ball is thrown will it return to the ground?

• 9.2

• 6

• 4.5

• 4