QUADRATIC EQUATIONS
The Ultimate High School Algebra Cheat Sheet & Exam Study Guide
1. The Standard Form & Core Concepts
Every quadratic equation can be written in the Standard Form:
ax2 + bx + c = 0 (where a ≠ 0)
• a controls the direction and width of the parabola.
• b shifts the vertex along an orbital path.
• c is the exact y-intercept of the graph.
2. The Big 4 Solving Methods
A. The Quadratic Formula (Works for EVERY equation!)
x = [-b ± √(b2 - 4ac)] / 2a
B. Factoring (FOIL in Reverse)
Find two numbers that multiply to give c and add up to give b (when a = 1).
Example: x2 - 5x + 6 = 0 → (x - 2)(x - 3) = 0 → x = 2 or x = 3
C. Completing the Square
Move the constant to one side, then add (b/2)2 to both sides to make a perfect square trinomial.
Useful for shifting Standard Form into Vertex Form.
D. Square Root Property
Use if b = 0 (no standalone x term). Isolates the square.
Example: x2 - 9 = 0 → x2 = 9 → x = ±3
The Ultimate High School Algebra Cheat Sheet & Exam Study Guide
1. The Standard Form & Core Concepts
Every quadratic equation can be written in the Standard Form:
ax2 + bx + c = 0 (where a ≠ 0)
• a controls the direction and width of the parabola.
• b shifts the vertex along an orbital path.
• c is the exact y-intercept of the graph.
2. The Big 4 Solving Methods
A. The Quadratic Formula (Works for EVERY equation!)
x = [-b ± √(b2 - 4ac)] / 2a
B. Factoring (FOIL in Reverse)
Find two numbers that multiply to give c and add up to give b (when a = 1).
Example: x2 - 5x + 6 = 0 → (x - 2)(x - 3) = 0 → x = 2 or x = 3
C. Completing the Square
Move the constant to one side, then add (b/2)2 to both sides to make a perfect square trinomial.
Useful for shifting Standard Form into Vertex Form.
D. Square Root Property
Use if b = 0 (no standalone x term). Isolates the square.
Example: x2 - 9 = 0 → x2 = 9 → x = ±3
