Answer
a. $y=-4x^2+50x$
b. $156$, the car will travel 156 feet after 6 second from the brake being applied.
Work Step by Step
a. Step 1. With the function $y=ax^2+bx+c$ and the given points, we have
$\begin{cases} a+b+c=46 \\ 4a+2b+c=84 \\ 9a+3b+c=114 \end{cases}$
Step 2. Subtract the first equation from the second and third to eliminate $c$
$\begin{cases} 3a+b=38 \\ 8a+2b=68 \end{cases}$ or $\begin{cases} 3a+b=38 \\ 4a+b=34 \end{cases}$
Step 3. Eliminate $b$ by subtraction, we have $a=-4$; back substitute to $b=50$ and $c=0$. Thus the function is $y=-4x^2+50x$
b. At $x=6$, we have $y=-4(6)^2+50(6)=156$; this means that the car will travel 156 feet after 6 second from the brake being applied.
