Explaining 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?

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?

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

A model rocket is launched from ground level. Its height, h meters above the ground, is a function of time t seconds after launch and is given by the equation h = −4.9t² + 68.6t.

What would be the maximum height, to the nearest meter, attained by the model?

• 243

• 242

• 241

• 240

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 swimmer’s dive off a 10-foot platform into a diving pool is modeled by the equation

y = 2x² − 12x + 10, where x represents the number of seconds since the swimmer left the diving board and y represents the number of feet above or below the water’s surface.

What is the farthest depth below the water’s surface that the swimmer will reach?

• 6 feet

• 8 feet

• 10 feet

• 12 feet

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