Quadratic equation
High School
Definition
An equation that is to the second degree polynomial. A standard quadratic equation looks like this, \(ax^2+bx+c=0\). There can be two variables to the second degree such as \(3x^2-5y^2+1=0\). It is considered a quadratic equation as long as the highest degree of polynomial is two.
Worked examples
\(2x^2 - 5x + 3 = 0\)
A standard quadratic equation with \(a=2\), \(b=-5\), \(c=3\); highest degree is 2.
\(x^2 = 16\)
Still quadratic even when \(b=0\) and \(c=0\); rewrite as \(x^2 - 16 = 0\).
\(3x^2 - 5y^2 + 1 = 0\)
Two variables, both squared — still quadratic because the highest degree is 2.
Common mistakes
- \(x^3 - 4x^2 + 2 = 0\) is quadratic → \(x^3 - 4x^2 + 2 = 0\) is cubic (degree 3) Quadratic means highest degree is exactly 2, not higher.
- \(5x + 7 = 0\) is quadratic → \(5x + 7 = 0\) is linear (degree 1) A quadratic must have an \(x^2\) term; degree 1 is linear.
- All quadratic equations must have three terms → \(x^2 - 9 = 0\) is quadratic with two terms Only the \(x^2\) term is required; \(b\) or \(c\) can be zero.
Where you'll use it next
You'll solve quadratic equations by factoring, completing the square, and the quadratic formula; graph parabolas in algebra and precalculus; and model projectile motion and optimization in physics and calculus.
Found in 3 StudyPug lessons
Solving Quadratic Equations by Factoring: A Comprehensive Guide
11th Grade11thGrade 11 Math
Unlock the power of factoring to solve quadratic equations. Our step-by-step approach covers essential techniques, common pitfalls, and real-world applications to boost your algebra skills.
Applications of Quadratic Equations
11th Grade11thGrade 11 Math
Turn real-world situations, like falling objects, areas, and profits, into quadratic equations you can actually solve.
The Quadratic Formula
11th Grade11thGrade 11 Math
The quadratic formula solves any equation of the form a x squared plus b x plus c equals zero.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026