1.10: Completing the square and a modulus graph

Write $2x^{2} + 3x - 4$ in the form $a(x + b)^{2} + c$, where $a$, $b$ and $c$ are constants.

Hence write down the coordinates of the stationary point on the curve $y = 2x^{2} + 3x - 4$.

On the axes below, sketch the graph of $y = \left\lvert 2x^{2} + 3x - 4 \right\rvert$, showing the exact values of the intercepts of the curve with the coordinate axes.

Find the value of $k$ for which $\left\lvert 2x^{2} + 3x - 4 \right\rvert = k$ has exactly $3$ values of $x$.