3.9: Completing the square, sketch and three solutions

Show that $2x^{2} + x - 15$ can be written in the form $2\left(x + a\right)^{2} + b$, where $a$ and $b$ are exact constants to be found.

Hence write down the coordinates of the stationary point on the curve $y = 2x^{2} + x - 15$.

On the axes, sketch the graph of $y = \lvert 2x^{2} + x - 15 \rvert$, stating the coordinates of the points where the graph meets the coordinate axes.

Write down the value of the constant $k$ for which the equation $\lvert 2x^{2} + x - 15 \rvert = k$ has $3$ distinct solutions.