Quadratic Functions, Equations and Inequalities - Maximum and Minimum Values of General Quadratic Functions

A tank is firing rounds during a target practice. The height, \(h\) metres, of a projectile above the ground during flight is governed by the equation \(h=5t-\frac{1}{5}{{t}^{2}}\) where \(t\) is the time in seconds for the projectile in flight.

1. What is the maximum height achieved by a projectile?
2. Sketch the curve \(h=5t-\frac{1}{5}{{t}^{2}}\) for \(h\ge 0\).
3. Find the range of values of \(t\) for which a round is at least \(10\) metres above the ground.