Question 1192394
<br>
The coefficient of x^2 depends on the force of gravity.<br>
The coefficient of x is determined by the initial vertical velocity.<br>
The constant term is determined by the initial height.<br>
When the problem says the launchpad is adjusted, it means we are adjusting the initial height -- we are not changing the force of gravity or the initial velocity.<br>
So we need to find the value of c in the function {{{h(x)=-3x^2+24x+c}}} for which the height is 0 at x=9:<br>
{{{h(9)=-3(9^2)+24(9)+c=-243+216+c=0}}}
{{{-27+c=0}}}
{{{c=27}}}<br>
ANSWER: After the (height of) the launchpad is adjusted, the function that models the path of the water balloon (as a function of the horizontal distance from the launch pad) is {{{h(x)=-3x^2+24x+27}}}.<br>