Parabola Word Problems

A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t² + 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?

• 0.5 seconds

• 1 second

• 1.5 seconds

• 2 seconds

• 3 seconds

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air. The equation h = -2t² + 7t + 4 models the toy's height, h, from the ground at t seconds after he threw it. How high is the toy after 1 second?

• 2

• 4

• 9

• 10

• 15

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground? 

• 4 seconds

• -2 seconds

• -6 seconds

• 9 seconds

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

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?

• $6060

• $20

• $600

• $10,250

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

The height of a water balloon that is launched into the air is given by h(t) = -5x²+20x+25. When will the balloon explode on the ground?

• 5 seconds

• 1 second

• 2 seconds

• 3 seconds

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

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.CED.A.1

CCSS.HSA.REI.D.10

CCSS.HSA.SSE.A.1

CCSS.HSS.ID.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?

Tags

CCSS.HSA.SSE.A.1

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?

Tags

CCSS.HSA.REI.D.10

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.REI.B.4

CCSS.HSA.SSE.A.1