## Precalculus (6th Edition)

t $=$ $\frac{ v_{0}±\sqrt {(v_{0})^{2}+ 64(s_{0}-h)}}{32}$
We need to solve the quadratic equation $h$ $=$ $-$$16$$t^{2}$ $+$ $v_{0}$$t + s_{0}. Shift the h from Left Hand Side (LHS) to Right Hand Side (RHS), so that the equation becomes, -$$16$$t^{2} + v_{0}$$t$ $+$ $s_{0}$ $-$$h = 0 We will use the quadratic formula to solve this equation. The quadratic formula is as follows, \frac{ -b ±\sqrt {b^{2}- 4ac}}{2a} Here a$$=$ $-$16 $b$ $=$ $v_{0}$ $c$ $=$ $s_{0}$$-$$h$ Putting the following in quadratic formula, we get $\frac{ -(v_{0}) ±\sqrt {(v_{0})^{2}- 4(-16)(s_{0} - h)}}{2(-16)}$ Solving the above, we get t $=$ $\frac{ v_{0}±\sqrt {(v_{0})^{2}+ 64(s_{0}-h)}}{32}$