Mary, I think the vertex is the highest or lowest point. I seem to remember using differentation to solve these so..

y = x^2 - 2x + 36
dy/dx = 2x - 2

at the turning point, dy/dx = 0 so

2x - 2 = 0
x = 1

substituting for x...
y = 1 -2 + 36 = 35

I hope thats right... that was about as far as I got with maths before walking out of school and it was a long while ago...

Jon