Quadratic Function

A quadratic function is a polynomial function of degree

2

that can always be written in the form

y = a x^{2} + b x + c,

with

a \neq = 0 .

Note that the highest exponent of the independent variable is

2 .

The graph of any quadratic function is a vertical parabola.

There are three ways to write a quadratic function.

Name	Equation	Characteristics
Standard Form	$y = a x^{2} + b x + c$	$a,$ $b,$ and $c$ are real numbers, $a \neq = 0,$ and $c$ is the $y -$ intercept of the parabola.
Vertex Form	$y = a (x - h)^{2} + k$	$a,$ $h,$ and $k$ are real numbers, $a \neq = 0,$ and $(h, k)$ is the vertex of the parabola.
Intercept Form (also called Factored Form)	$y = a (x - x_{1}) (x - x_{2})$	$a,$ $x_{1},$ and $x_{2}$ are real numbers, $a \neq = 0,$ and $x_{1}$ and $x_{2}$ are the $x -$ intercepts of the parabola.

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