Applications of Quadratic Equations

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

Rafael kicks a ball in the air. This equation represents the approximate height, in meters, of the ball above the ground after t seconds.

h(t) = -5t² + 45t

How long is the ball in the air?

• 0 seconds

• 3 seconds

• 9 seconds

• 45 seconds

A diver is standing on a platform above the pool. He jumps from the platform with an initial upward velocity of 8 ft/s.

h(t) = −16t² + 8t + 24

The function h(t) represents his height above the water in feet after t seconds.

What was the initial height of the diver?

• 0.25 ft

• 24 ft

• 25 ft

• 8 ft

The path of an arrow is represented by the function, where h(t) is the height of the arrow (in feet) after t seconds.

h(t) = -16t² +20t + 6

When will the arrow hit the ground?

• 6 seconds

• 20 seconds

• -0.25 seconds

• 1.5 seconds

A lizard is jumping across the water in search of food. The function below models the lizard's height (in feet) above the water t seconds after he jumps.

h(t) = -12t² + 6t

How long after jumping is he back on the water?

• 12 seconds

• 0.25 seconds

• 0.50 seconds

• 6 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

What is the maximum height of the rocket?

• 4 feet

• 0 feet

• 128 feet

• 256 feet

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 below, where x is the price of each ticket.

p(x)= -15x² +600x +60

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

• $6060

• $20

• $600

• $10,250

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

You jumped of a cliff into the ocean. The height of your jump (in feet) after t seconds is modeled by the function:

h(t) = -16t² + 22t + 20

How fast would you reach the water after you jump?

• 8 seconds

• 1 second

• 2 seconds

• 0.625 seconds