Mathematics » Differential Calculus » Sketching Graphs

# 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