01 Key Concepts
Standard Form
ax^2 + bx + c = 0, where a is not 0.
Solving by Factoring
Factor the quadratic, then set each factor equal to zero and solve — this works using the Zero Product Property.
Zero Product Property
If the product of two factors equals zero, at least one of the factors must itself equal zero.
Solving 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.
Number of Solutions
A quadratic can have two real solutions, one repeated real solution, or no real solutions (only complex ones), depending on its discriminant.
02 Key Formulas
- Standard form: ax^2 + bx + c = 0
- Zero Product Property: if p*q=0, then p=0 or q=0
03 Solved Examples
Example 1 Solve x^2 + 5x + 6 = 0 by factoring.
- Factor: x^2+5x+6 = (x+2)(x+3).
- Set each factor to zero: x+2=0 or x+3=0.
- Solve each: x=-2 or x=-3.
Answer: x = -2 or x = -3
Example 2 Solve x^2 - 9 = 0 by factoring.
- Factor as a difference of squares: (x+3)(x-3) = 0.
- Set each factor to zero: x+3=0 or x-3=0.
Answer: x = -3 or x = 3
Example 3 Solve x^2 = 49 by taking square roots.
- Take the square root of both sides: x = plus or minus sqrt(49).
- sqrt(49) = 7.
Answer: x = 7 or x = -7
04 Practice Questions
1Solve x^2 + 7x + 10 = 0 by factoring.
x=-2 or x=-5
2Solve x^2 - 16 = 0.
x=4 or x=-4
3Solve x^2 = 64.
x=8 or x=-8
4Solve x^2 - 5x + 6 = 0 by factoring.
x=2 or x=3
5What property lets you solve a factored quadratic equation?
The Zero Product Property
📄 Quadratic Equations — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.