How do you solve #x^2 - 18x + 81 = 0# graphically?
The vertex is
We begin with
Well, for vertex form, we could "complete the square". I'm a big fan of this method, but I always got to factoring first, and if that doesn't work I move on to other methods like completing the square or the quadratic formula.
So, let's begin with factoring.
We are trying to factor
So, the factors of
No, out of these factors we are supposed to have them add to
There it is.
So, that means we can rewrite
No, look: there is no stretch factor for
To find other points, just replace
If we solve for when
Now you have the vertex and a couple of point to help guide you as you draw your graph
If you want to double check this, just graph it