Quadratic Functions, Equations and Inequalities

A quadratic graph has \(x\)-intercepts at \((-1,0)\) and \((5,0)\). It passes through \((0,5)\).

1. Find its equation in factorised form.

2. Express its equation in completed-square form and find its turning point.

3. The horizontal line \(y=k\) is drawn.

   Find the values of \(k\) for which the line intersects the graph:

   1. twice;

   2. exactly once;

   3. not at all.

   Explain your answers.