Write the equation in vertex form to find the maximum height, as well as the time when the maximum height is reached.
The vertex form of a quadratic equation is:
[tex]y=a(x-h)+k[/tex]Where (h,k) is the vertex of the parabola, k is the maximum or minimum value and h is the value of x where that maximum or minimum is reached.
To write h in vertex form, complete the square:
[tex]\begin{gathered} h(t)=-5t^2+30t \\ =-5(t^2-6t) \\ =-5(t^2-6t+9-9) \\ =-5((t-3)^2-9) \\ =-5(t-3)^2-5(-9) \\ =-5(t-3)^2+45 \end{gathered}[/tex]We can see that in this case, the vertex is (3,45).
Therefore:
1)
[tex]h(t)=-5(t-3)^2+45[/tex]2)
The ball reaches the maximum height 3 seconds after being hit.
