Quadratic Applications Warmup

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 

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

• 1

• 3

• 2

• 5

• 4

A function is shown. f(x) = x² - 6x -27.

Fill in the blanks below to make the statement true.

"The graph of f(x) has a minimum value of ​ (a)   and has zeros at ​ (b)   and ​ (c)   ​

• -27

• -36

• -33

• -42

• -9

• -3

• 0

• 3

• 9

• 4

A ball is thrown vertically into the air. Its height in feet after t seconds is given by the equation h(t) = –5t² + 20t. How many feet into the air will the ball be at 3 seconds?

Mathematical Equivalence

OFF

Which of the following represents a quadratic function?

Analyze the given graph and the determine the correct function.​ (a)   ​ (b)  

• x(x-2)

• x+(x-2)

• (x+4)(x+5)

• (x-0)