Quadratics

# SAT Math — Quadratic Equations and Functions ## What Is a Quadratic? A quadratic is any equation or function where the highest power of the variable is 2. The standard form is: y = ax² + bx + c Quadratics produce parabolas (U-shaped curves) when graphed. They appear in the Digital SAT Math section — 2 modules × 35 minutes = 70 minutes total, 44 questions. The Digital SAT Math section is adaptive: Module 1 covers a broad difficulty range; Module 2 difficulty is set by Module 1 performance. Quadratics are classified under the "Advanced Math" content domain, which is one of the four Math content areas (Algebra, Advanced Math, Problem-Solving & Data Analysis, Geometry & Trigonometry). ## Three Key Forms of a Quadratic | Form | Equation | What it tells you directly | |---|---|---| | Standard | y = ax² + bx + c | Y-intercept (c); direction (a > 0 = opens up, a < 0 = opens down) | | Factored | y = a(x − r)(x − s) | Roots/x-intercepts: r and s | | Vertex | y = a(x − h)² + k | Vertex (h, k); axis of symmetry x = h | You need to be comfortable converting between all three forms. ## Finding Roots: Factoring When ax² + bx + c = 0, find two numbers that: - Multiply to give a × c - Add to give b Example: x² + 5x + 6 = 0 - Multiply to 6, add to 5: the numbers are 2 and 3 - Factor:…