A rocket on a computer screen has a path modeled by the equation \(h=-t^2+3t+10\) where t is time in seconds and h is the height above a platform and is in computer units. Find how long the rocket takes to reach the platform.

The platform is reached when \(h = 0\). It is necessary to solve the equation \(0=-t^2+3t+10\). Hence \((t - 5)( t + 2) = 0\). Solving the equation gives \(t = 5\) or \(-2\). As t is a time it is not possible for t to be \(-2\). The rocket takes \(5\) seconds to reach the platform.