An object is launched upward with the height function h(t) = -16t² + 64t + 5, where h is in feet and t is in seconds. What is the object's…

The maximum of a downward-opening parabola is at its vertex, at $t=-\frac{b}{2a}=-\frac{64}{2(-16)}=2$ seconds. Then $h(2)=-16(4)+64(2)+5=-64+128+5=69$ feet, choice D. Choice A ($5$) is the launch height at $t=0$. Choice B ($64$) is the coefficient of $t$, the initial speed, not a height. Choice C ($128$) is the middle term $64(2)$ alone, without subtracting the $64$ lost to gravity. The vertex formula gives the time of the peak, and you must then substitute that time back into $h$ to get the height.