Quadratic Formula — SAT Math Explained
A universal formula that gives the solutions of any quadratic equation ax² + bx + c = 0: x = (-b ± √(b² - 4ac)) / (2a). It always works, regardless of whether the quadratic factors nicely.
The Core Idea
The ± symbol means you compute two solutions — one using addition, one using subtraction. The formula is derived from completing the square on the general form of a quadratic.
Key Vocabulary
Indicates two separate calculations — one with + and one with -
b² - 4ac, the expression under the radical — determines the nature of solutions
The square root symbol √
Exact leaves the radical; approximate rounds to a decimal
Step-by-Step: How to Approach Quadratic Formula
Ensure the equation is in standard form: ax² + bx + c = 0
Identify a, b, and c (be careful with signs!)
Calculate the discriminant: b² - 4ac
Substitute a, b, and the discriminant into the formula
Simplify the numerator and denominator separately
Write both solutions using + and -
Simplify radicals if possible; approximate if needed
When To Use Quadratic Formula
When the quadratic doesn't factor easily
When you need exact decimal values
When the discriminant check shows no rational roots
When working in real-world problems requiring precision
Common Errors to Avoid
Forgetting the negative sign in front of b (writing +b instead of -b)
Only dividing part of the numerator by 2a instead of the entire expression
Using the wrong sign for b, c when they appear negative in the equation
Practice: Quadratic Formula
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