Solving Quadratics 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

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

What is the initial (starting) height of an object following this path?  h(t) = -16t² +20t + 6

• -16 feet 

• 0 feet

• 20 feet 

• 6 feet 

You and some friends went to a haunted house on Halloween. The mummy scared one friend so much that she jumped into the air! The equation h = -4t² + 2t models her jump where h is her jump's height in feet t seconds after the mummy scares her. When did she reach her maximum height?

• 0.1 seconds

• 0.25 seconds

• 0.50 seconds

• 1 second

• 2 seconds

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation: h = -16t^2 + 80 About how long did it take for the balloon to hit the ground?

• 1.73 seconds

• 2.24 seconds

• 2.45 seconds

• 2.83 seconds

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

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds. When is the ball at ground level?

• only at t = 0 seconds

• only at t = 3 seconds

• only at t = 9 seconds

• at both t = 0 seconds and t = 3 seconds

Given the equation for a thrown ball h=15+22t-5t², how long will it take to hit ground?

• 2

• 3

• 4

• 5

Select the solutions to the equation

4x² + 11x + 7 = 0

• x = - 1.75

• x = 6

• x = - 1

• x = 1