Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Preliminary Questions - Page 602: 3

The maximum height is $$y= 4.$$

The particle’s height is $y = 4 − t^2$. Now, to find the maximum height, we put the derivative equal to zero, that is, $y'=-2t=0$, then $t=0$. Hence, the maximum height is $$y(0)=4-0^2=4.$$