Factored Form of a Quadratic Function

A quadratic function is said to be written in factored form, or intercept form, if it follows a specific format.

Here, and are real numbers with The value of gives the direction of the parabola. When the parabola faces upward, and when it faces downward. The zeros of the parabola are and and the axis of symmetry is the vertical line

Example

Consider the graph of

Comparing the generic factored form with the example function, the values of

and

can be identified.

These values determine the characteristics of the parabola shown in the graph.

Direction	Zeros	Axis of Symmetry
	and
Since is greater than the parabola opens upward.	The zeros are and Therefore, the parabola intersects the axis at and	The axis of symmetry is the vertical line

Extra

Consider other example quadratic functions.

Although these functions do not strictly follow the format of the factored form, they are said to be written in factored form because they can easily be rewritten in the desired format.

Function	Function	Function

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Example

Extra