# What is a quadratic function?

Jul 3, 2018

General form of a quadratic function is $f \left(x\right) = a {x}^{2} + b x + c$

#### Explanation:

Is a function with this general expresion and his characteristics are

a) Is defined for all $x \in \mathbb{R}$. So $D o m f = \mathbb{R}$
b) Plot is a parabola with y-intercept y in $\left(0 , c\right)$
c) The x-intercepts depends on the value of discriminant $\Delta$ defined by $\Delta = {b}^{2} - 4 a c$

If $\Delta = 0$ only has a single x-intercept
if $\Delta > 0$ has two x intercept
if $\Delta < 0$ then has not any x-intercept

The branches of parabola are oriented upwards if $a > 0$ or downwards if $a < 0$
The general look of this type of functions is as follows (particular case of ${x}^{2} - 3 x - 3 = f \left(x\right)$
graph{x^2-3x-3 [-12.66, 12.65, -6.33, 6.33]}
Hop this helps