# What is the vertex form of #y=6x^2+13x+3 #?

##### 1 Answer

The general formula for vertex form is

You can also find the answer by completing the square, the general formula is found by completing the square in using

#### Explanation:

The vertex form is given by

where

This form highlights the transformations that the function

The vertex form is also form in which a quadratic function can be directly solved algebraically (if it has a solution). So getting a quadratic function into vertex form from standard form, called completing the square, is the first step to solving the equation.

The key to completing the square is building a perfect square in ANY quadratic expression. A perfect square is of the form

Examples

COMPLETING THE SQUARE

You start with

factor out the 6

Multiply and divide the linear term by 2

This lets us see what our

To build our perfect square we need the

we add this to our expression, but to avoid changing the value of anything we must subtract it too, this creates an extra term,

We gather up our perfect square

and replace it with

We multiple out our extra to to get it outside the brackets.

Play with some fractions to neaten

And we have

If we want to in the identical form as above

The general formula used above is from doing the above with