What is the vertex of #y= x^2 - 4x + 1#?
We start off with
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
And the vertex is
Bit of allowed shortcut that relies on the principles behind completing the square. I will let you work out
Consider the standard form of:
Write this as:
In your question
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