A cubic function has the standard form of f(x) = ax3 + bx2 + cx + d. The "basic" cubic function is f(x) = x3. 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.
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?
Created by peer tutors under the direction of Learning Centre faculty at Douglas College, British Columbia.