Quadratic Applications

A fountain shoots water in an arc over a lake that can be modeled by the graph of the equation y= -0.4x² + 8x where x is the horizontal distance (in feet) from the fountain base and y is the height (in feet) above the river.  How high does the water go?

• It goes 11.78 feet high

• It goes 20 feet high

• It goes 40 feet high

• It goes 10 feet high

If I want to see the initial height of an object, I should _____________.

• Substitute x = 0 into the equation and evaluate.

• Use x = (-b /2a) as my answer.

• Find the y-coordinate of the vertex. 

• Set my equation = 0 and solve.

A raft is dropped from a helicopter 256 feet in the air above the ocean.  Its approximate height, h, after t seconds is given by the function h(t) = -16t² + 256.  How many seconds did it take the raft to hit the water? 

• -4

• 2

• 4

• 8

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

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(t) = -16t² +128t  
When will the object reach its maximum height?

• 4 ft

• 0 seconds

• 0 ft

• 4 seconds

A ball is thrown into the air with an upward velocity of 100 ft/s. Its height, h, after t seconds is given by the function
 h = -16t² + 64t + 960.
How many seconds did it take for the ball to reach its maximum height?

• 10 seconds

• 64 seconds

• 960 seconds

• 2 seconds

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t² + 90t gives the height h of the ball after t seconds.
What is the maximum height of the ball?

• 126.56 ft

• 5.625 sec

• 2.81 sec

• 90 ft

Based on the table, which function can best be used to model this situation?

• h(t) = 99t² + 858

• h(t) = -4.9t² + 295t + 0.6

• h(t) = -4.9t² + 295t + 2

• h(t) = 99t² + 1,470.3

What is the starting height of a ball that follows the path y = -16x² + 8x + 5 ?

• 8 ft

• 5 ft

• Not enough information

• 4 ft

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t² + 90t gives the height h of the ball after t seconds.
How many seconds will it take the ball to hit the ground?

• 126.56 ft

• 5.625 sec

• 2.81 sec

• 0 ft