1.3: Completing the square and a modulus graph

Write $x^{2} - 9x + 8$ in the form $(x - p)^{2} - q$, where $p$ and $q$ are constants.

Hence write down the coordinates of the minimum point on the curve $y = x^{2} - 9x + 8$.

On the axes below, sketch the graph of $y = \left\lvert x^{2} - 9x + 8 \right\rvert$, showing the coordinates of the points where the curve meets the coordinate axes.

Write down the value of $k$ for which $\left\lvert x^{2} - 9x + 8 \right\rvert = k$ has exactly 3 solutions.