Quadratic Equations
A quadratic equation has the form ax² + bx + c = 0. Its graph is a U-shaped curve called a parabola.
Standard Form
ax² + bx + c = 0 (a ≠ 0)
Solutions are called roots or zeros — the x-values where the parabola crosses the x-axis.
Solving by Factoring
Factor the quadratic into two binomials, set each to zero.
x² + 5x + 6 = 0
(x + 2)(x + 3) = 0
x = −2 or x = −3
The Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
2x² − 4x − 6 = 0: a=2, b=−4, c=−6
x = (4 ± √(16+48)) / 4 = (4 ± 8) / 4
x = 3 or x = −1
The Discriminant
b² − 4ac tells you the number of solutions:
> 0: two real solutions
= 0: one real solution (vertex touches x-axis)
< 0: no real solutions (parabola doesn't cross x-axis)
FAQ
Can every quadratic be factored? No — use the quadratic formula when it can't be factored nicely.
Quick Quiz
Test what you just learned. Choose the best answer for each question.