Quadratic Function Word Problems

The height of a rocket, at selected times, is shown in the table above. Based on these data, which statement is not a valid conclusion?

• The rocket was launched from a height of 180 feet.

• The maximum height of the rocket occurred 3 seconds after launch.

• The rocket was in the air approximately 6 seconds before hitting the ground.

• The rocket was above 300 feet for approximately 2 seconds.

Morgan throws a ball up into the air. The height of the ball above the ground, in feet, is modeled by the function h(t) = −16t² + 24t, where t represents the time, in seconds, since the ball was thrown. What is the appropriate domain for this situation?

An archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t) = -16t² + kt + 3. If the maximum height of the arrow occurs at time t = 4, what is the value of k?

• 128

• 64

• 8

• 4

The expression -4.9t² + 50t + 2 represents the height, in meters, of a toy rocket t seconds after launch. The initial height of the rocket, in meters, is

• 0

• 2

• 4.9

• 50

The height, y, of a ball tossed into the air can be represented by the equation y = −x² + 10x + 3, where x is the elapsed time. What is the equation of the axis of symmetry of this parabola?

• y = 5

• y = -5

• x = 5

• x = -5

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

The height of a ball Doreen tossed into the air can be modeled by the function h(x) = −4.9x² + 6x + 5, where x is the time elapsed in seconds, and h(x) is the height in meters. The number 5 in the function represents

• the initial height of the ball

• the time at which the ball reaches the ground

• the time at which the ball was at its highest point

• the maximum height the ball attained when thrown in the air

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:

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

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

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