# What is the vertex form of #y=16x^2+14x+2#?

##### 1 Answer

I have shown the solution in a lot of detail so you can see where everything comes from. With practice you can do these a lot faster by skipping steps!

#### Explanation:

Given:

write as

Take the 16 outside the bracket giving:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This is where we start to change things but in doing so we introduce an error. This is mathematically corrected later on

At this stage it is not correct to say that it is the correct value for y

Divide what is inside the bracket by

Now halve the

Now square the bracket

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In doing this we have introduced an error. This can be 'got round' like this:

Let

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As both (1) and (2) equal

Squaring the bracket

Multiplying the contents of the bracket by 16

we can cancel values that are the same on each side of the equals sign.

We are left with:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So the vertex form is: