Where the Formulas Come From · Hard problem

A ball is thrown upward at $64$ feet per second from a height of $6$ feet. Its height after $t$ seconds is $h(t) = -16t^2 + 64t + 6$.

(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.