Explaining Quadratic Function Word Problems

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

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

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

Tags

CCSS.HSF-IF.C.7A

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

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

How long would it take you to hit the water?

• 8 seconds

• 1 second

• 1.5 seconds

• 1/4 second

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

When would you reach 16 feet above the water?

• 8 seconds

• 1 second

• 1/2 second

• 1/4 second

A diver is standing on a platform above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Use the formula: h(t) = −16 t² + 8t + 24. How high is the platform?

• .25 ft

• 24 ft

• 25 ft

• 8 ft