Quadratics — Three Forms, One Concept

Standard form: y = ax2 + bx + c

c = y-intercept. "a" tells you if parabola opens up (positive) or down (negative).

Factored form: y = a(x - r)(x - s)

r and s are the x-intercepts (roots/zeros/solutions).

Vertex form: y = a(x - h)2 + k

(h, k) is the vertex — the maximum or minimum point.

Quadratic formula: x = (-b plus or minus sqrt(b2 - 4ac)) / 2a

Discriminant: b2 - 4ac

Positive = 2 real solutions

Zero = 1 real solution (vertex touches x-axis)

Negative = no real solutions

SAT loves asking: How many solutions? Just compute the discriminant — no need to actually solve.

Reference:

Wikipedia: Quadratic Equation

https://en.wikipedia.org/wiki/Quadratic_equation