Quadratic Functions
A quadratic function is a rule that can be written in the form,
y =
or f(x) = 
Ax^{2} + Bx + C Ax^{2} + Bx + C 
where A, B, and C are real numbers and A
≠ 0.
For example, the following are quadratic functions:

Here A = 2, B
, and CThe following are functions but they are not quadratic functions:.

y = 4x^{2} + 5 
Here A = 4, B = 0, and C = 5. 
f(x) = x^{2} + 2x  8 
Here A = 1, B = 2, and C = 8. 
The following are functions but they are not quadratic functions:
Note:
Notice that in a quadratic function the
variable is in the numerator and the
coefficient of the x^{2} term is not zero.
Note that y = 4x^{2} + 5 can be written as
y = 4x^{2} + 0x + 5.
You may need to simplify a function to
determine if it is quadratic. For example:
f(x) 
= x^{3} + x(5x  x^{2}) + 6
= x^{3} + 5x^{2}  x^{3} + 6
= 5x^{2} + 6 
This is a quadratic function because it can
be written in the form f(x) = Ax^{2} + Bx + C where A = 5, B = 0, and C
= 6.
