vertex = (h,k) = (2,-3)
vertex form of equation: y = a(x - h)2 + k = a(x - 2)2 - 3
Based on the vertex, you know that the parabola will have a minimum or maximum at the point (2,-3). If the x2 term is positive, the parabola will extend upwards and cross the x-axis, creating x-intercepts. If the x2 term is negative, the parabola will extend downwards and not cross the x-axis. Set a as any negative number so that the parabola doesn't have any x-intercepts.
y = -(x - 2)2 - 3 = -x2 + 4x - 4 - 3 = -x2 + 4x - 7