# Quadratic Functions

In this lesson, we will learn

- the different forms of quadratic functions
- general form
- factored form
- vertex form

- how to convert from general form to factored form.
- how to convert from the general form to the vertex form using the vertex formula.
- how to convert from the general form to the vertex form using completing the square.

**Forms of Quadratic Functions**
We can write quadratic functions in different ways or forms.

- General Form
- Factored Form
- Vertex Form

The general form of a quadratic equation is

y = *ax*^{2} + *bx* + c where *a*, *b* and *c* are real numbers and *a* is not equal to zero.

For example,
*y* = 2*x*^{2} + 5*x* − 30

The factored form of a quadratic equation is

y = *a*(*x* + *b*)(*x* + c) where *a*, *b* and *c* are real numbers and *a* is not equal to zero.

For example, *y* = 2(*x* + 6)(*x* − 5).

The factored form is useful because we can see the *x*-intercepts (which are also the roots when the function is zero).

For example, the *x*-intercepts of *y* = *a*(*x* + *b*)(*x* + c) are (−*b*, 0) and (−*c*, 0)

The vertex form of a quadratic equation is

y = *a*(*x *−* h*)^{2} + *k* where *a*,* h *and* k *are real numbers and *a* is not equal to zero.

For example, *y* = 2(*x* + 6)^{2} − 5.

The vertex form is useful because we can see the turning point or vertex of the graph.

For example, the turning point or vertex of *y* = *a*(*x *−* h*)^{2} + *k* is (*h*, *k*). If *a* is positive then it is a minimum vertex. It *a* is negative then it is a maximum vertex.

The following video looks at the various formats in which Quadratic Functions may be written as.

## General Form to Factored Form

The following videos show how to change quadratic functions from general form to factored form.

## General Form to Vertex Form by using the Vertex Formula

We can change a quadratic function from general form to vertex form by using the vertex formula.

Example of how to convert standard form to vertex form of a parabola equation.

## General Form to Vertex Form by Completing the Square

We can change a quadratic function from general form to vertex form by completing the square.

The following video shows how to use the method of Completing the Square to convert a quadratic function from standard form to vertex form.

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