Question

Last one!! I need the steps please! Will mark brainliest!

Answer 1

Answer:

$h(t)=-6(t-2)^2+24$

Step-by-step explanation:

Given function:

$h(t)=-6t^2+24t$

where:

• h = height (in feet)
• t = times (in seconds)

Rewrite in the form $h(t)=a(t-h)^2+k$

The quickest way to do this is to expand $h(t)=a(t-h)^2+k$ and compare coefficients with the original function.

$\begin{aligned}h(t)& =a(t-h)^2+k\\ & = at^2-2aht+ah^2+k\end{aligned}$

Comparing coefficients with $h(t)=-6t^2+24t$

$\begin{aligned}\implies at^2& =-6t^2\\ a &=-6\end{aligned}$

$\begin{aligned}\implies -2aht & =24t\\ -2(-6)ht& =24t\\ 12ht & = 24t\\ 12h & = 24\\ h & = 2\end{aligned}$

$\begin{aligned}\implies ah^2+k & = 0\\(-6)(2)^2+k &=0\\ -24+k & =0\\ k &=24 \end{aligned}$

Therefore, substituting the found values into the equation:

$h(t)=-6(t-2)^2+24$