A ball's height in feet after t seconds is modeled by h(t) = -16t² + 64t + 5. What is the maximum height the ball reaches, in feet?

The height is a downward-opening parabola, so its maximum is at the vertex. The vertex occurs at $t = -\frac{b}{2a} = -\frac{64}{2(-16)} = 2$ seconds. Substitute: $h(2) = -16(4) + 64(2) + 5 = -64 + 128 + 5 = 69$ feet, choice B. Choice A (64) is the coefficient of $t$, not the height. Choice C (5) is the starting height at $t = 0$. Choice D (32) is the height gained at $t = 1$ from the linear term, or half of 64, and ignores both the quadratic term and the initial 5 feet. Only the value at the vertex gives the true maximum.