algebra
What is a Quadratic Equation?
January 12, 2026
4 min read
PanMaths Team
Definition
A quadratic equation is any equation that can be written in the formax² + bx + c = 0 where a ≠ 0.
💡Key Point
The "quad" in quadratic means "square" — every quadratic equation must have an x² term!
Three Forms
1
ax² + bx + c = 0Standard Form — Most common, used with quadratic formula
2
a(x - h)² + k = 0Vertex Form — Shows the vertex of the parabola
3
a(x - r₁)(x - r₂) = 0Factored Form — Shows the roots directly
Is It Quadratic?
| Equation | a | b | c | Quadratic? |
|---|---|---|---|---|
| x² - 5x + 6 = 0 | 1 | -5 | 6 | ✓ Yes |
| 2x² + 3x = 0 | 2 | 3 | 0 | ✓ Yes |
| 3x + 5 = 0 | — | 3 | 5 | ✗ No |
Why Does "a" Matter?
If a = 0, the x² term disappears and you're left with a linear equation (like 3x + 5 = 0), not a quadratic. That's why we require a ≠ 0.
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