Cubic Equations Worksheet
A Grade 10 Math worksheet focusing on understanding, solving, and graphing cubic equations.
Includes
Standards
Cubic Equations: Grade 10 Algebra
Name:
Date:
Score:
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.
Related Worksheets
Solving Square Root Equations
This worksheet focuses on solving square root equations, including identifying extraneous solutions, for Grade 10 Algebra students.
Perfect Square Trinomials Worksheet
This worksheet focuses on identifying, factoring, and creating perfect square trinomials for Grade 10 Algebra students.
Radical Operations Worksheet
Grade 10 Math worksheet covering operations with radical expressions including simplification, addition, subtraction, multiplication, and division.
Rearranging Equations Worksheet
A Grade 10 Math worksheet focused on rearranging algebraic equations to solve for specific variables.
Zero Product Property Worksheet
Practice applying the Zero Product Property to solve quadratic equations and other polynomial equations.
Sigma Notation Practice
A Grade 10 math worksheet focusing on understanding and applying sigma notation for sums and series.
Intercepts Exploration
Explore and identify x-intercepts and y-intercepts of linear equations and graphs.
Equations with Variables on Both Sides
Practice solving linear equations with variables on both sides, including those with fractions and decimals.