What is the vertex form of a quadratic equation, and what do each of its components represent?

y = a(x - h)² + k, where (h, k) is the vertex of the parabola and 'a' determines the direction and width of the opening.

Using the quadratic formula, what are the solutions to ax² + bx + c = 0?

x = (−b ± √(b² − 4ac)) / 2a. Both the plus and minus cases must be considered to find all solutions.

What does the discriminant (b² − 4ac) tell you about the solutions of a quadratic equation?

If positive, two real solutions; if zero, exactly one real solution (a repeated root); if negative, no real solutions (two complex solutions).

How do you convert a quadratic from standard form ax² + bx + c to vertex form by completing the square?

Factor out 'a' from the first two terms, add and subtract (b/2a)² inside the parentheses, then rewrite as a(x − h)² + k.

If a parabola has x-intercepts at x = p and x = q, what is its factored form?

y = a(x − p)(x − q), where 'a' is determined by another point on the parabola (such as the y-intercept).

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SAT Advanced Math Mastery

Master the Advanced Math section of the SAT with 28 targeted flashcards covering nonlinear functions, polynomial operations, rational equations, and more. These cards focus on the exact concepts tested on the SAT, helping students build the skills needed to tackle the hardest math questions on the exam.

29 cards Intermediate Quadratic Equations & Functions Polynomials & Their Operations Rational & Radical Expressions Exponential & Other Nonlinear Functions Systems & Nonlinear Equations Functions & Their Graphs

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