Mathematics » Differential Calculus » Sketching Graphs

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

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

d24d40e4e1002a1f21b8bb7ad891e0e8.png

[Attributions and Licenses]


This is a lesson from the tutorial, Differential Calculus and you are encouraged to log in or register, so that you can track your progress.

Log In

Share Thoughts