Mastering Quadratic Equations
Quadratic equations—those of the form ax² + bx + c = 0—appear frequently in the advanced SAT Math section. There are three primary methods for solving them. Factoring works best when the equation factors cleanly: for example, x² - 5x + 6 = 0 factors to (x - 2)(x - 3) = 0, giving solutions x = 2 or x = 3. When factoring isn't obvious, complete the square by moving the constant, dividing all terms by 'a', adding (b/2a)² to both sides, then taking the square root. For any quadratic, you can always use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. The discriminant (b² - 4ac) tells you how many real solutions exist: positive means two, zero means one, negative means none. The SAT often disguises quadratics in word problems—look for phrases like 'the product of two consecutive integers' or parabolic motion. Practice recognizing these contexts to apply the right method efficiently under timed pressure.