Quadratic Functions, Equations and Inequalities - Quadratic Inequalities

A soldier throws a grenade during training. The height, \(h\) metres, of the grenade above the ground during flight is governed by the equation \(h=\frac{25}{4}t-\frac{5}{2}{{t}^{2}}\) where \(t\) is the time in seconds for the grenade in flight.

1. What is the maximum height achieved by a grenade?
2. Sketch the curve \(h=\frac{25}{4}t-\frac{5}{2}{{t}^{2}}\) for \(t\ge 0\) and \(h\ge 0\) .
3. Find the range of values of \(t\) for which the grenade is at least \(1\) metres above the ground.