How do you write #y=3x^2-18x+5# in vertex form?
(That's what vertex form is in the textbook here. Other forms are possible.)
Your teacher probably wants you to complete the square. (It is an important technique, used for other things also.)
This method relies on the fact that:
If the stuff in parentheses is going to be a perfect square
So the stuff inside parentheses is not a perfect square becuase it is missing
Now, (within limits) we are in charge here! We will add
It looks like this:
Now regroup, keeping the perfect square were we want it to be. (We're in charge (within limits).)
(Convince yourself that this really is equal to what we started with. Do the algebra to simplify it.)
Now we'll write it this way:
And there's our answer.
(If your class uses a different vertex for, it's probably:
Depends on your knowing the vertex formula (which was 'discovered' by completing the square).
(Why> Well, start with
(I now, I do arithmetic kinda weird.)