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.

Tags

CCSS.HSA.SSE.A.1

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?

• $0\le t\le1.5$

• $0\le t\le9$

• $0\le h\left(t\right)\le1.5$

• $0\le h\left(t\right)\le9$

Tags

CCSS.HSF.IF.B.5

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?

• $0\le x\le2.5$

• $0<x<5.5$

• $2.5<x<5.5$

• $x\ge2$

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.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

Tags

CCSS.HSA.SSE.A.1

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

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.HSA.REI.B.4

CCSS.HSA.SSE.A.1

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.REI.D.11

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

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

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.IF.B.4