What's the maximum height in feet that the projectile will reach?

Question

If a projectile is launched from a platform 8 feet above the ground with an initial velocity of 64 feet per second, then its trajectory can be modeled by the equation h=-16t²+64t+8, where h represents the height of the projectile t seconds after it was launched. Based on this model, what's the maximum height in feet that the projectile will reach?

Answer 1

Observe that the trajectory is an upside-down parabola, so the maximum height occurs at the vertex.

 

Use the formula   t_vertex = -b/(2a) and take that t-value (indep. variable) into the formula for y to get y_vertex, the maximum height in feet.