Key Features of Quadratic Functions in the Real World

How high would you jump if the equation for jumping from the roof of a house is the following:

h(t) = -16t² + 8t + 32?

• 12 ft.

• 32 ft.

• 8 ft.

• 26 ft.

How fast would you reach the water if you jump off a cliff using the formula: h(t) = -16t² + 8t + 32?

• 8 seconds

• 3 seconds

• 1.7 seconds

• 1/4 second

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?

• $60

• $6060

• $600

• $10,250

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation, where h is the height of the balloon and t is the time in seconds since the balloon was dropped. h = -16t² + 80 About how long did it take for the balloon to hit the ground?

• 1.73 seconds

• 2.24 seconds

• 2.45 seconds

• 2.83 seconds

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

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

The height of a flare can be approximated by the function h = -16t² + 96t, where h is the height if feet and t is the time in seconds. Find the time it takes the flare to hit the ground.

• 3 seconds (find the maximum)

• 6 seconds (find the zero)

• 144 seconds (find the maximum)

• 0 seconds (find the zero)

Does the following quadratic equation have a maximum or minimum value? How can you tell?

y= x² + 2x - 3

• Minimum value, because the a value is positive

• Maximum value, because the b value is positive

• Maximum value, because the a value is positive

• Minimum value, because the c value is negative

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -8t² + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

• 1 foot

• 5 feet

• 7 feet

• 8 feet