Factor, evaluate and interpret polynomial expressions with checked algebraic identities.
Before you begin
Factor polynomials, use exponent laws and solve equations with domain restrictions.
Worked example
Sketch y = (x + 2)³. Mark its intercept on the x-axis and the points one unit to either side. Describe end behavior.
Diagram not to scale.
Shift the graph of y = x³ horizontally to x = -2.
Evaluate at x = h − 1, h and h + 1.
The positive leading cubic coefficient determines the end behavior.
Answer: x-intercept (-2, 0); points (-3, −1) and (-1, 1). Left end down; right end up.
Check your result using the method in the example before moving to the next question.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
Easy: Start with the preview and follow the worked example.
Medium: Practice the same exercise types with a fresh numbered set.
Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
Sketch y = (x - 1)³. Mark its intercept on the x-axis and the points one unit to either side. Describe end behavior.
Diagram not to scale.
2
Sketch y = (x + 0)³. Mark its intercept on the x-axis and the points one unit to either side. Describe end behavior.
Diagram not to scale.
3
Sketch y = (x - 2)³. Mark its intercept on the x-axis and the points one unit to either side. Describe end behavior.
Diagram not to scale.
4
Sketch y = (x + 1)³. Mark its intercept on the x-axis and the points one unit to either side. Describe end behavior.
Diagram not to scale.
5
Sketch y = (x + 2)³. Mark its intercept on the x-axis and the points one unit to either side. Describe end behavior.
Diagram not to scale.
6
Sketch y = (x + 1)³. Mark its intercept on the x-axis and the points one unit to either side. Describe end behavior.
Diagram not to scale.
Answer Key
1. x-intercept (1, 0); points (0, −1) and (2, 1). Left end down; right end up.2. x-intercept (0, 0); points (-1, −1) and (1, 1). Left end down; right end up.3. x-intercept (2, 0); points (1, −1) and (3, 1). Left end down; right end up.4. x-intercept (-1, 0); points (-2, −1) and (0, 1). Left end down; right end up.5. x-intercept (-2, 0); points (-3, −1) and (-1, 1). Left end down; right end up.6. x-intercept (-1, 0); points (-2, −1) and (0, 1). Left end down; right end up.