Question

A model rocket is launched from the roof of a building. Its flight path is modeled

by h = -5t^2 +30t +10 where h is the height of the rocket above the ground in
metres and r is the time after the launch in seconds.
What is the rocket's maximum height?

Answer 1

55

Explanation:

This is the equation of a parabola. To make things simpler, we can replace
`h` with
`y` and
`t` with
`x`. Therefore,
`y=-5x^2+30x+10`. Because the coefficient of the
`x^2` term is negative, we know the parabola points down, and the maximum height is the vertex. The x coordinate of the vertex of a parabola can be found with the equation
`-(b)/(2a)`, or
`-(30)/(-10) = 3`. Plugging in
`3` into the equation gives us
`y = -5(3)^2+30(3)+10 = \boxed{55}`