C1 - sketching a graph

Question: Sketch the graph of y=x^2-6x+3, giving the coordinates of the minimum point.

Since I can't factorise it normally, I used the quadratic formula and got 3+root6 or 3-root6. I'm not sure how to continue from here. Do I sub the values into the quadratic to find the value of y for each one? Then the minimum point is the one lowest in the graph?

The x value of the minimum point is the mean of the two roots but this is a laborious way to find it. Do you know how to complete the square? This gives the coordinates of the minimum immediately.

Completing the square would give (x-3)^2 -6.

Yes so the coordinates of the minimum are (3, -6).

In general, when $y=(x-a)^2+b$ the minimum is $(a, b)$.

What about for maximum point?

Completing the square gives the location of the maximum of a parabola too.

http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-completingsquare1-2009-1.pdf