Answer: First option.
Step-by-step explanation:
You know that the following function model the height "h" of the ball (in feet) after a time "t" (in seconds):
[tex]h=-16t^2+48t+8[/tex]
Notice that it is a Quadratic function, therefore, it is a parabola.
Then, the x-coordinate of its vertex will give you the time in seconds in which the balll reaches its maximum height and the y-coordinate of the vertex will give you the ball's maximum height.
You can find the x-coordinate of the vertex with this formula:
[tex]x=t=\frac{-b}{2a}[/tex]
You can identify that:
[tex]a=-16\\b=48[/tex]
Substituting values, you get:
[tex]x=t=\frac{-48}{2(-16)}=1.5[/tex]
FInally, you must substiute this value into the Quadratic function and then evaluate in order to find the ball's maximum height.
This is:
[tex]h=-16(1.5)^2+48(1.5)+8=44[/tex]
