Question

On top of a hill, a rocket is launched from a distance 80 feet above a lake. The rocket will fall into the lake after its engine burns out. The rocket's height, h, in feet above the surface of the lake, is given by the equation, h = -16t 2 + 64t + 80, where t is time in seconds. The maximum height of the rocket is a0 feet.

Answer 1

what do you need to find here ?

Answer 2

the height of the rocket

Answer 3

This is in the form of,
\(\normalsize\color{blue}{y = -16x^2 + 64x + 80 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{y = -16x^2 + 64x + 64+16 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{y = -16x^2 + 64x -64+64+ 64+16 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{y = -16(x^2 -4x +4)+64+ 64+16 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{y = -16(x^2 -4x +4)+144 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{y = -16(x-2)^2+144 \LARGE\color{white}{ \rm │ }}\)

Answer 4

The maximum point is (2,144)

Answer 5

If maximum point is (2,144) then what does that mean for the rocket height ?

Answer 6

Im very confused

Answer 7

Do you know what a maximum point of a parabola is ?