Quadratic Function: Factored Form

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 is r1 and r2, then the function is y = a(x - r1)(x - r2).

If the x-intercepts of a quadratic function are
r1 and r2,
then the quadratic function in factored form is
y = a(x - r1)(x - r2).

Example 1

Find the x-intercept of the given function. y = x^2 - 2x - 3

Set '(quadratic function) = 0'.

This means finding the intersecting points of
y = x2 - 2x - 3 and y = 0 (x-axis).

The answer is the intersecting point's x values.

So solve x2 - 2x - 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 x2 term is (+): +1.
So draw a parabola which is opened upward.

Example 2

Find the x-intercept of the given function. y = -x^2 + 10x - 25

Set '(quadratic function) = 0'.

Solve -x2 + 10x - 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 x2 term is (-): -1.
So draw a parabola which is opened downward.