Where the Formulas Come From · Hard problem

A ball is thrown upward at $32$ feet per second from a height of $5$ feet. Its height after $t$ seconds is $h(t) = -16t^2 + 32t + 5$.

(a) When does it reach its highest point?   (b) How high is that?   (c) When does it hit the ground? Give seconds to two decimal places.