# Quadratic Function: Factored Form

How to write a quadratic function in factored form: formula, examples, and their solutions.

## Formula

If the *x*-intercepts of a quadratic function are*r*_{1} and *r*_{2},

then the quadratic function in factored form is*y* = *a*(*x* - *r*_{1})(*x* - *r*_{2}).

## Example 1

Set '(quadratic function) = 0'.

This means finding the intersecting points of*y* = *x*^{2} - 2*x* - 3 and *y* = 0 (*x*-axis).

The answer is the intersecting point's *x* values.

So solve *x*^{2} - 2*x* - 3 = 0.

*x* = -1, 3.

So the given quadratic function is*y* = (*x* + 1)(*x* - 3).

To graph *y* = (*x* + 1)(*x* - 3):

Point the *x*-intercepts on the *x*-axis: -1, 3.

The coefficient of the *x*^{2} term is (+): +1.

So draw a parabola which is opened upward.

## Example 2

Set '(quadratic function) = 0'.

Solve -*x*^{2} + 10*x* - 25 = 0.

*x* = 5.

So the given quadratic function is*y* = -(*x* - 5)(*x* - 5),*y* = -(*x* - 5)^{2}.

To graph *y* = -(*x* - 5)^{2}:

Point the *x*-intercept on the *x*-axis: 5.

The coefficient of the *x*^{2} term is (-): -1.

So draw a parabola which is opened downward.