What is a quadratic function?

1 Answer
Jul 3, 2018

General form of a quadratic function is #f(x)=ax^2+bx+c#

Explanation:

Is a function with this general expresion and his characteristics are

a) Is defined for all #x in RR#. So #Dom f = RR#
b) Plot is a parabola with y-intercept y in #(0, c)#
c) The x-intercepts depends on the value of discriminant #Delta# defined by #Delta=b^2-4ac#

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^2-3x-3=f(x)#
graph{x^2-3x-3 [-12.66, 12.65, -6.33, 6.33]}
Hop this helps