Question

A volleyball reaches its maximum height of 13 feet, 3 seconds after its served. Which of the following quadratics could model the height of the vollyball over time after it is served. Select all that apply.

A: f(x)=2x^2+12x+5
B: f(x)=-2x^2+12x-5
C: f(x)=-2x^2-12x+5
D: f(x)=-2(x-3)^2+13
E: f(x)=-2(x+3)^2+13

Answer 1

B: f(x)=-2x^2+12x-5

and!!!!!!

D: f(x)=-2(x-3)^2+13

Explanation:

b and are the only ones that give you the values 13 and 3

Answer 2

If it reaches its maximum height a t=3 its velocity must be zero at t=3

dy/dx=0 at t=3

dA/dx=4x+12=24 at t=3 so this does not apply

dB/dx=-4x+12=0 at t=3 and B=13 at t=3 so B applies

dC/dx=-4x-12=-24 at t=3 so this does not apply

dD/dx=-4x-12=-24 at t=3 so this does not apply

dE/dx=-4x-12=-24 at t=3 so this does not apply

So only quadratic B: reaches a maximum height of 13 feet at 3 seconds.