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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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A quadratic function is a rule that can be written in the form,

 y = or f(x) = Ax2 + Bx + CAx2 + 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 = 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:

Note:

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:
 f(x) = 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 = 6.