# What is the vertex of #y= x^2 - 4x + 1#?

##### 2 Answers

#### Explanation:

We start off with *vertex form*. And, because I like easier, more time-saving routes, I'll do that.

How we do that is by completing the square.

The first step is to get the coefficient of

Now we have the second step. Something you should know is that the goal of completing the square is to make the

So now we have the value that will make

*PLEASE NOTE* I added and then subtracted the

Now, we can condense

From here, finding the vertex is very simple: take the value in the parentheses

To find the

graph{y=x^2-4x+1}

And the vertex *is*

Bit of allowed shortcut that relies on the principles behind completing the square. I will let you work out

#### Explanation:

Consider the standard form of:

Write this as:

In your question

now apply:

Then substitute

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

Your

so

So

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

With practise you could work this bit out in your head. As long as the equation is in the format I showed you.

I will let you work out the value for