In these lessons, we will learn

- the different forms of quadratic functions (general, factored and vertex forms)
- 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.

**Related Pages**

Quadratic Formula

Graphs Of Quadratic Functions

Factoring Out Common Factors

More Algebra Lessons

Math Worksheets

The following diagram shows how to use the vertex formula to convert a quadratic function from general form to vertex form. Scroll down the page for more examples and solutions for quadratic equations.

**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.

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

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.

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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