You have to complete the square on this to get the (h, k) of the vertex. Start by setting the thing equal to 0 and then moving the 2 over to the other side. This is [tex] x^{2} -x=-2[/tex]. Now take half the linear term (the linear term is 1, so half of that is 1/2), square it (1/4) and add it to both sides. Now we have a parabola that looks like this: [tex] x^{2} -x+ \frac{1}{4} =-2+ \frac{1}{4} [/tex]. By doing this we have created a perfect square binomial on the left. This binomial will be shown along with the addition of the right side of the equation: [tex](x- \frac{1}{2}) ^{2}=- \frac{7}{4} [/tex]. Now move the right side back over to the left by addition and set it back equal to y to get this as your final equation: [tex](x- \frac{1}{2}) ^{2}+ \frac{7}{4} =y [/tex]. That's called "work" form or vertex form and the vertex from that is easily discernible as [tex]( \frac{1}{2} , \frac{7}{4} )[/tex]. The y-coordinate is of course the second value in that set of parenthesis!
