You would best do this by completing the square on the quadratic and subbing in the vertex they give you, like this:
[tex]2(x- \frac{3}{2})^{2} = \frac{18}{4}-c [/tex]
Since the y coordinate of the vertex is 1/2 and we need to solve for c, set the [tex] \frac{18}{4}-c [/tex] equal to 1/2 and solve for c, which is the whole point of what we are doing, right?
[tex] \frac{18}{4}-c= \frac{1}{2} [/tex] and [tex] \frac{18}{4}- \frac{2}{4}=c [/tex]
[tex] \frac{16}{4}=c [/tex] and c = 4. So that's our answer!
