Question 1199226
We can model the path of the baseball as a parabola. The maximum height is the y-coordinate of the vertex of the parabola, and the distance of the baseball from home plate when it is at its maximum height is the x-coordinate.
For a quadratic {{{ax^2+bx+c}}}, the vertex is at {{{-b/2a}}}. In this case, {{{b=1}}} and {{{a=-0.0032}}}. Plugging this into a calculator, we see that {{{-b/2a}}} is {{{156.25}}}, which is the x-coordinate of the vertex. To get the y-coordinate, we simply put in {{{x=156.25}}} into the quadratic, to get {{{y=81.125}}}. Therefore, the maximum height of the baseball is {{{highlight(81.125)}}} feet, and it is {{{highlight(156.25)}}} feet from the home plate when it happens.