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
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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
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Mastering the Quadratic Formula: Your Key to Solving Quadratic Equations
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Unlock the power of the quadratic formula to solve any quadratic equation. Our comprehensive guide offers clear explanations, step-by-step instructions, and practice problems to boost your algebra skills.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026