A **cubic function** has the standard form of f(x) = ax^{3} + bx^{2} + cx + d. The "basic" **cubic function is** f(x) = x^{3}. You can see it in the graph below. In a cubic function, the highest power over the x variable(s) is 3.

The coefficient "a" functions to make the graph "wider" or "skinnier", or to reflect it (if negative): The constant "d" in the equation is the y-intercept of the graph.

**Exercise A: **

In the interactive graph below, graph cubic functions using the included table of values. For the given function and **x** values, calculate **y **values and explore how the graph looks. Press the "new problem" button for a new function.

By Samantha Cruz.

Manipulate the sliders to change the values of **a**, **h** and **k** for ** y**= a ( **x**-h )^{3} +k. How do a, h and K change the shape of the function?