Answer:
A)
Step-by-step explanation:
Given function:
[tex]h(t)=-16t^2+75t+25[/tex]
The domain (input values) will be the x-intercepts, so the values of t when h(t) = 0.
The quickest way to find these is to use the quadratic formula.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\implies t=\dfrac{-75 \pm \sqrt{75^2-4(-16)(25)} }{2(-16)}[/tex]
[tex]\implies t=\dfrac{-75 \pm \sqrt{7225}}{-32}[/tex]
[tex]\implies t=\dfrac{75 \pm 85}{32}[/tex]
[tex]\implies t=5, t=-\dfrac{5}{16}[/tex]
Time cannot be negative.
When h(t) = 0, the disk will hit the floor.
Therefore, the domain is restricted to 0 ≤ t ≤ 5
