If your vertex is 2, -5 that is your h,k. The point of 4,7 is your x,y. From there you just plug in and solve for a. Once you find a, you rewrite the equation including the a, h, and k so the only variables left are y and x. In that way, it is still an equation because you have 2 variables, and the equation can be reused with any new points that it passes through.