Quadratic Equations — Factoring, Formula, Completing the Square

SAT Math · Axiom Academy

Quadratic Equations: Three Methods Factoring, Quadratic Formula & Completing the Square A quadratic equation is any equation in the form: The goal: Find the value(s) of that make the equation true. These values are called solutions or roots . Factoring - Quickest if it works Quadratic Formula - Always works, requires memorization Completing the Square - Useful for specific SAT questions The quadratic factors nicely (SAT usually designs them this way) You need speed on a timed test The coefficients are small integers When factoring doesn't work or you need certainty, use the Quadratic Formula : Pronounced: "x equals negative b plus-or-minus the square root of b-squared minus 4ac, all over 2a" If discriminant > 0: Two real solutions ✓ If discriminant = 0: One real solution (repeated root) ✓ If discriminant < 0: No real solutions (complex solutions) ✓ When to Use Quadratic Formula: Factoring is too hard or impossible Discriminant tells you about solutions before computing Method 3: Completing the Square ✓ When to Use Completing the Square: SAT asks for vertex form (finding the turning point) Deriving the quadratic formula itself Minimizing or maximizing a quadratic in context Method Comparison: Which Should You Use? Reliability: Only if it factors Effort: Medium (must memorize) Effort: High (arithmetic-heavy) First: Try to factor (fast check for common patterns) Second: If no obvious factors, use quadratic formula

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