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Algebra
Quadratic Equations Cheat Sheet
Complete quadratic equations cheat sheet with quadratic formula, factoring methods, completing the square, graphing parabolas, and vertex form. Free PDF download.
Standard Forms
| Name | Formula | Notes |
|---|---|---|
| Standard Form | General quadratic equation | |
| Vertex Form | Vertex at (h, k) | |
| Factored Form | Roots at r₁ and r₂ | |
| Intercept Form | x-intercepts at p and q |
The Quadratic Formula
| Name | Formula | Notes |
|---|---|---|
| Quadratic Formula | Solves ax² + bx + c = 0 | |
| Discriminant | Determines nature of roots | |
| Two Real Roots | Two distinct real solutions | |
| One Real Root | One repeated real solution | |
| Complex Roots | Two complex conjugate solutions |
Vieta's Formulas
| Name | Formula | Notes |
|---|---|---|
| Sum of Roots | ||
| Product of Roots | ||
| Reconstruct Equation | From known roots |
Completing the Square
| Name | Formula | Notes |
|---|---|---|
| Step 1 | Factor out a from first two terms | |
| Step 2 | Add and subtract (b/2a)² | |
| Step 3 | Factor perfect square |
Parabola Properties
| Name | Formula | Notes |
|---|---|---|
| Vertex x-coordinate | x-value of vertex | |
| Vertex y-coordinate | y-value of vertex | |
| Axis of Symmetry | Vertical line through vertex | |
| Direction | ||
| y-intercept | Where parabola crosses y-axis |
Special Factoring
| Name | Formula | Notes |
|---|---|---|
| Difference of Squares | ||
| Perfect Square | ||
| AC Method | Split middle term |
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