Answer:
After 22 seconds the projectile reach its maximum height of 4,840 units
Step-by-step explanation:
we have
[tex]h(t)=-10t^{2}+440t[/tex]
This is a vertical parabola downward (because the leading coefficient is negative)
The vertex is a maximum
Find out the coordinates of the vertex
Convert the quadratic equation in vertex form
Factor -10
[tex]h(t)=-10(t^{2}-44t)[/tex]
Complete the square
[tex]h(t)=-10(t^{2}-44t+22^2)+(10)(22^2)[/tex]
[tex]h(t)=-10(t^{2}-44t+22^2)+4,840[/tex]
Rewrite as perfect squares
[tex]h(t)=-10(t-22)^{2}+4,840[/tex]
The vertex is the point (22,4,840)
therefore
After 22 seconds the projectile reach its maximum height of 4,840 units
