Find the axis of symmetry
Well, it's a parabola. If you rewrite the equation by completing the square, you get
y = (x - 7/2)^2 + 2 - (7/2)^2
= (x - 7/2)^2 - 41/4
It will be symmetric about the x = 7/2 line and the minimum will be at y = -41/4.