Cubic Equations Worksheet
A Grade 10 Math worksheet focusing on understanding, solving, and graphing cubic equations.
Includes
Standards
Cubic Equations: Grade 10 Algebra
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. A cubic equation is a polynomial equation of degree .
2. The general form of a cubic equation is ax³ + bx² + cx + d = .
3. A cubic equation can have at most real roots.
4. Which of the following is a cubic function?
f(x) = 2x² + 3x - 1
g(x) = x³ - 4x + 5
h(x) = 5x⁴ - x³ + 2
k(x) = x + 7
5. Find the real roots of the equation x³ - 6x² + 5x = 0 by factoring.
6. Use the Rational Root Theorem to find all possible rational roots of the equation x³ - 2x² - 5x + 6 = 0. Then, find the real roots.
7. A cubic function's graph always has at least one real x-intercept.
True
False
8. The end behavior of a cubic function with a positive leading coefficient is that it rises to the right and falls to the left.
True
False
9. Sketch the graph of a cubic function with three distinct real roots. Label the x-intercepts as -2, 0, and 3.