### Instruction: A ball travels on a parabolic path in which the height (in feet) is given by the expression $-25t^2+75t+24$, where $t$ is the time after launch. At what time is the height of the ball at its maximum?### Response: I know that this is a quadratic function, and it has a maximum value at the vertex of the parabola.
To find the vertex, I can use the formula $t=-\frac{b}{2a}$, where $a$ and $b$ are the coefficients of $t^2$ and $t$ respectively.
In this case, $a=-25$ and $b=75$, so $t=-\frac{75}{2(-25)}=\frac{3}{2}$.
That means the ball reaches its maximum height 1.5 seconds after launch.