Quadratic Applications

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation 
s(t) = –16t² + 64t + 80.
What will be the object's maximum height? 

• 2 ft

• 80 ft

• 144 ft

• 64 ft

A lizard is jumping across the water in search of food. The equation h = -12t² + 6t models the lizard's height in feet above the water t seconds after he jumps. How long after jumping is he back on the water?

• 0.1 seconds

• 0.25 seconds

• 0.50 seconds

• 0.75 seconds

• 1 second

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

When I want to find the maximum or minimum height of an object, I should_____.

• Set the equation = 0 and solve.
• Use x = (-b/2a) as my answer.
• Substitute x = 0 into the equation.
• Find the y-coordinate for the vertex.

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

A rock is dropped from a bridge 320 ft. above a river. The pathway that the rock takes can be modeled by the equation h = -16t² + 320. How long will it take for the rock to reach the river (i.e. hit the "ground")?

• 2.5 sec

• 3.5 sec

• 4.5 sec

• 3.8 sec

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t² +84t + 100 models the height, h, of the fireworks at any given time, t. How high do the fireworks get?

• 2.625

• 6.25

• 100

• 200

• 210.25