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PSAT Math: Advanced Math and Geometry

Quadratic Expressions and Equations

Advanced Math is the second major category in PSAT Math. Quadratic expressions take the form ax² + bx + c. Factoring: find two numbers that multiply to ac and add to b. For example, x² + 5x + 6 = (x + 2)(x + 3) because 2 × 3 = 6 and 2 + 3 = 5. The quadratic formula: x = (−b ± √(b² − 4ac)) / 2a. The discriminant b² − 4ac tells you about solutions: positive → two real solutions, zero → one real solution (double root), negative → no real solutions. Completing the square converts a quadratic to vertex form: y = a(x − h)² + k, where (h, k) is the vertex. In PSAT contexts, quadratics model projectile motion, revenue vs. cost, and area optimization problems.

PSAT Math: Advanced Math and Geometry

Quadratic Expressions and Equations

Advanced Math is the second major category in PSAT Math. Quadratic expressions take the form ax² + bx + c. Factoring: find two numbers that multiply to ac and add to b. For example, x² + 5x + 6 = (x + 2)(x + 3) because 2 × 3 = 6 and 2 + 3 = 5. The quadratic formula: x = (−b ± √(b² − 4ac)) / 2a. The discriminant b² − 4ac tells you about solutions: positive → two real solutions, zero → one real solution (double root), negative → no real solutions. Completing the square converts a quadratic to vertex form: y = a(x − h)² + k, where (h, k) is the vertex. In PSAT contexts, quadratics model projectile motion, revenue vs. cost, and area optimization problems.