Glossary
Quadratic equation
Also written: quadratic · quadratics · second degree equation
Definition
A quadratic equation is one that can be written as ax squared plus bx plus c = 0, with a not equal to zero. The squared term is what makes it quadratic rather than linear.
Standard form
The condition matters: if were zero the term would vanish and the equation would be linear, not quadratic.
Why there are usually two solutions
A quadratic graphs as a parabola, a U-shaped curve. Solving means finding where it meets the -axis, and a U can cross a horizontal line twice, touch it once, or miss it entirely. Those three cases are exactly what the discriminant predicts.
Three ways to solve one
| Method | Best when |
|---|---|
| Factoring | you can spot a whole-number factor pair |
| Completing the square | you need vertex form, a maximum, or a minimum |
| The quadratic formula | always works, so use it when the others stall |
All three give the same answers. They differ in speed, and in what else they reveal along the way.
Lessons that use this term
- The Quadratic Formula: How and Why It Works
Learn the quadratic formula, where it comes from, and how to use it to solve any quadratic equation, with worked examples and practice problems.
- Solving Quadratic Equations by Factoring
Solve quadratics by factoring using the zero product property, why the equation must equal zero first, and how to factor the common trinomial patterns.
- Completing the Square, Step by Step
Learn completing the square: why the method works geometrically, how to handle a leading coefficient, and how it produces vertex form and the quadratic formula.