Graphing Cubic Functions
Graph cubic functions in Grade 9 algebra by plotting key points including the inflection point, identifying end behavior based on the leading coefficient, and recognizing the S-shaped curve.
Key Concepts
New Concept A cubic function is a polynomial function in which the greatest power of any variable is 3. What’s next Next, you'll see how these functions behave by graphing the parent function, $y=x^3$, and using its graph to solve equations.
Common Questions
What are the key features of a cubic function graph?
A cubic function y = ax³ + bx² + bx + d has an S-shaped curve, an inflection point where the curve changes concavity, and end behavior where one end goes to +∞ and the other to -∞. Unlike parabolas, cubics have no maximum or minimum.
How does the leading coefficient affect a cubic function's graph?
If a > 0, the graph falls to the left and rises to the right. If a < 0, it rises to the left and falls to the right. This is the opposite of the pattern for even-degree functions like quadratics.
What points are most useful when graphing a cubic function?
Plot the y-intercept (x=0), any x-intercepts (where y=0), and a few additional points on both sides. For y = x³, key points are (-2,-8), (-1,-1), (0,0), (1,1), (2,8), which reveal the S-shape clearly.