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

Only selections B and D give a maximum height of 13 at t=3. However, both of those functions have the height be -5 at t=0, meaning the ball was served from 5 ft below ground. This does not seem like an appropriate model.

We suspect ...
• the "correct" answers are probably B and D
• whoever wrote the problem wasn't paying attention.

Answer 2

Answer:

D.

Step-by-step explanation:

Intuitively it's a volleyball game reaching its maximum height, then we must discard the 1st option because of its parameter a >0, and whenever a>0 the parabola makes a curve, rather different than in a volleyball game.

Also, considering Vertex of this parabola by (-b/2a, -Δ/4a) given the fact that the question says the maximum height.

Taking

y= height in feet

x= time in second

Function Vertex (-b/2a, -Δ/4a)=(-3, -13)

A: f(x)=2x²+12x+5 False

B: f(x)=-2x²+12x-5 Function Vertex (-b/2a, -Δ/4a) = (3,23) False

C: f(x)=-2x²-12x+5  Function Vertex (-b/2a, -Δ/4a) = (-3,23) False

D: f(x)=-2(x-3)²+13 Function Vertex (-b/2a, -Δ/4a) = (3,13) True

E: f(x)=-2(x+3)²+13 Function Vertex (-b/2a, -Δ/4a) =(-3,13) False