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

Answer:

55

Step-by-step 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 $-\frac{b}{2a}$, or $-\frac{30}{-10} = 3$. Plugging in $3$ into the equation gives us $y = -5(3)^2+30(3)+10 = \boxed{55}$