2.1 - Quadratic Functions

Vertex

The point where the axis of symmetry passes through a parabola.

Discriminant

b2 - 4ac Perfect Square - Quadratic is factorable

Coordinates of the Vertex

x-coordinate : -b/2a y-coordinate: f(-b/2a)

Intercept Form of a Quadratic Equation

y = (x - p) (x - q) p & q - x-intercepts of the parabola

Standard (Vertex) Form of a Quadratic Equation

y = a (x - h)^2 + k h - x-coordinate of the vertex k - y-coordinate of the vertex

General Form of a Quadratic Equation

y = ax2 + bx + c c - y-intercept

Axis of Symmetry

A vertical line that divides the parabola into two equal halves.

Computing the X-Intercepts of a Quadratic Function in General Form

1) Set equation equal to zero 2) Compute the discriminant 3) If discriminant is a perfect square, then solve by factoring 4) If discriminant is not a perfect square, then solve using the quadratic formula

Quadratic Function

A quadratic function is one of the form f(x) = ax^2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.