1.9: Modulus quadratic graph and three solutions

On the axes below, sketch the graph of $y = \left\lvert 3x^{2} - 14x - 5 \right\rvert$, showing the coordinates of the points where the graph meets the coordinate axes.

Find the exact value of $k$ such that $\left\lvert 3x^{2} - 14x - 5 \right\rvert = k$ has $3$ solutions only.