Question

The function y=−16x2+v0x models the height of a football in feet x seconds after a player kicks it. In the equation of the function, v0 is the ball's initial velocity in feet per second. The ball hits the ground 2 seconds after the player kicks it. What is the value of ​ v0 ​?

Answer 1

16x^2-vox=0 when x=2 so

16x^2-vox=0

64-2vo

64=2vo

vo=32 ft/s

Answer 2

The value of v₀ is 32.

Explanation:

The height of a football in feet x seconds after a player kicks it, is defined by the function

`y=-16x^2+v_0x`

It is given that the ball hits the ground 2 seconds after the player kicks it. The height is 0 at x=2.

`0=-16(2)^2+v_0(2)`

`0=-64+2v_0`

`64=2v_0`

Divide both sides by 2.

`32=v_0`

Therefore the value of v₀ is 32.