## Functions of the Form \(y = ax^{3} + bx^{2} + cx + d\)

## Optional Investigation: The effects of \(a\) on a cubic function

Complete the table below and plot the graphs of \(f(x)\) and \(g(x)\) on the same system of axes.

Be careful to choose a suitable scale for the \(y\)-axis.

\[f(x) = 2x^{3} – 5x^{2} – 14x + 8 \qquad \qquad g(x) = -2x^{3} + 5x^{2} + 14x – 8\]

\(x\) | \(-\text{3}\) | \(-\text{2}\) | \(-\text{1}\) | \(\text{0}\) | \(\text{1}\) | \(\text{2}\) | \(\text{3}\) | \(\text{4}\) | \(\text{5}\) |

\(f(x)\) | \(-\text{25}\) | ||||||||

\(g(x)\) | \(\text{25}\) |

**The effects of \(a\) on a cubic graph**