Answer
a. $y=-16x^2+40x+200$
b. $0$, the ball will hit the ground at 5 second.
Work Step by Step
a. Step 1. With the function $y=ax^2+bx+c$ and the given points, we have
$\begin{cases} a+b+c=224 \\ 9a+3b+c=176 \\ 16a+4b+c=104 \end{cases}$
Step 2. Subtract the first equation from the second and third to eliminate $c$
$\begin{cases} 8a+2b=-48 \\ 15a+3b=-120 \end{cases}$ or $\begin{cases} 4a+b=-24 \\ 5a+b=-40 \end{cases}$
Step 3. Eliminate $b$ by subtraction; we have $a=-16$ and back substitute to get $b=40$ and $c=200$. Thus the function is $y=-16x^2+40x+200$
b. At $x=5$, we have
$y=-16(5)^2+40(5)+200=0$
this means that at $5$ seconds, the ball will hit the ground.
