Answer: After 3.75 seconds
Step-by-step explanation:
For a Quadratic function in the form [tex]f(x)=ax^2+bx+c[/tex], if [tex]a<0[/tex] then the parabola opens downward.
Rewriting the given function as:
[tex]h(t) = - 16t^2+120t[/tex]
You can identify that [tex]a=-16[/tex]
Since [tex]a<0[/tex] the the parabola opens downward.
Therefore, we can conclude that the x-coordinate of the vertex is the time in seconds in which the ball will reach the maximum height. You can find it with this formula:
[tex]t=\frac{-b}{2a}[/tex]
Substitute values, we get
[tex]t=\frac{-120}{2(-16)}=3.75\ seconds[/tex]
