Algebra · Quick Reference

Quadratic Equations Cheat Sheet

Algebra I · Lesson 8/17

In one line: a quadratic equation involves a variable raised to the second power — its graph is always a curved parabola, and it can have zero, one, or two real solutions.

Key Ideas

1Standard Form. ax^2 + bx + c = 0, where a is not 0.

2Solving by Factoring. Factor the quadratic, then set each factor equal to zero and solve — this works using the Zero Product Property.

3Zero Product Property. If the product of two factors equals zero, at least one of the factors must itself equal zero.

4Solving by Taking Square Roots. For equations of the form x^2 = k, take the square root of both sides, remembering both the positive and negative root.

5Number of Solutions. A quadratic can have two real solutions, one repeated real solution, or no real solutions (only complex ones), depending on its discriminant.

Worked Examples

Solve x^2 + 5x + 6 = 0 by factoring.

x = -2 or x = -3

Solve x^2 - 9 = 0 by factoring.

x = -3 or x = 3

Solve x^2 = 49 by taking square roots.

x = 7 or x = -7

Formulas

Standard form: ax^2 + bx + c = 0

Zero Product Property: if p*q=0, then p=0 or q=0

Practice Yourself

Solve x^2 + 7x + 10 = 0 by factoring.

x=-2 or x=-5

Solve x^2 - 16 = 0.

x=4 or x=-4

Solve x^2 = 64.

x=8 or x=-8