A quadratic function is a rule that can be written in the form,
or f(x) =
|Ax2 + Bx + C
Ax2 + Bx + C
where A, B, and C are real numbers and A
For example, the following are quadratic functions:
||Here A = 2, B
, and CThe following are functions but they are not quadratic functions:.
|y = 4x2 + 5
||Here A = 4, B = 0, and C = 5.
|f(x) = -x2 + 2x - 8
||Here A = -1, B = 2, and C = -8.
The following are functions but they are not quadratic functions:
Notice that in a quadratic function the
variable is in the numerator and the
coefficient of the x2 term is not zero.
Note that y = 4x2 + 5 can be written as
y = 4x2 + 0x + 5.
You may need to simplify a function to
determine if it is quadratic. For example:
||= x3 + x(5x - x2) + 6
= x3 + 5x2 - x3 + 6
= 5x2 + 6
This is a quadratic function because it can
be written in the form f(x) = Ax2 + Bx + C where A = 5, B = 0, and C