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.