Question

A rocket is launched from the ground. It reaches a maximum height of 45 meters in 3 seconds and then lands back on the ground after 6 seconds. What is the function, written in standard form,

that models the trajectory of the rocket? (use shift 6 for the power and no spaces)
f(x) = type your answer...

Answer 1

Check the picture below.

so from the provided information, we can say that the parabola has a vertex at (3 , 45) and it has a zero at (6 , 0) or we can say is just another point at (6 , 0)

`~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill`

`\begin{cases} h=3\\ k=45\\ \end{cases}\implies y=a(~~x-3~~)^2 + 45\hspace{4em}\textit{we also know that} \begin{cases} x=6\\ y=0 \end{cases} \\\\\\ 0=a(6-3)^2+45\implies -45=9a\implies \cfrac{-45}{9}=a\implies -5=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-5(x-3)^2 + 45 \end{array}} ~\hfill`