Quadratic Functions Word Problems Graph Interpretations

Jason jumpled off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function $$h\left(t\right)=-16t^2+16t+480$$ , where $$t$$ is the time in seconds and $$h$$ is the height in feet.

How long did it take for Jason to reach his maximum height? Type in only the value.

(a)  

Jason jumpled off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function $$h\left(t\right)=-16t^2+16t+480$$ , where $$t$$ is the time in seconds and $$h$$ is the height in feet.

What was the highest point that Jason reached? Only key in the value.

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height $$h$$ after $$t$$ seconds is given by the equation $$h\left(t\right)=-16t^2+128t$$ (if air resistance is neglected).

How long will it take for the rocket to return the ground?​ (a)  

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height $$h$$ after $$t$$ seconds is given by the equation $$h\left(t\right)=-16t^2+128t$$ (if air resistance is neglected).

After how many seconds will the rocket be 112 feet above the ground?​ (a)   and ​ (b)  

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height $$h$$ after $$t$$ seconds is given by the equation $$h\left(t\right)=-16t^2+128t$$ (if air resistance is neglected).

How long will it take the rocket to hit its maximum height? ​ (a)  

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height $$h$$ after $$t$$ seconds is given by the equation $$h\left(t\right)=-16t^2+128t$$ (if air resistance is neglected).

What is the maximum height?

A rocket is launched from atop a 101 foot cliff with an initial velocity of 116 ft/s.

Substitute the values into the vertical motion formula $$h\left(t\right)=-16t^2+vt+h_0$$ . Type your answer in using the variable x in place of t and y in place of h(t).

A rocket is launched from atop a 101 foot cliff with an initial velocity of 116 ft/s.

Using the formula provided, $$h\left(t\right)=-16t^2+116x+101$$ , how long will the rocket take to hit the ground after it is launched?

(a)  

You and a friend are hiking in the mountains. You want to climb to a ledge that is 20 feet above you. The height of the grappling hook you throw is given by the function $$h\left(t\right)=-16t^2+32t+5$$ .

What is the maximum height of the grappling hook? ​ (a)  

Can you throw it high enough to reach the ledge? ​ (b)   ​

You are trying to dunk a basketball. You need to jump 2.5 feet in the air to dunk the ball. The height that your feet are above the ground is given by the function $$h\left(t\right)=-16t^2+12t$$ .

What is the maximum height your feet will be above the ground? ​ (a)  

Will you be able to dunk the basketball? ​ (b)   ​