I'm asked to give the equation of a parabola when both the top (maximum?*) and a point on the line are given. The general form of a parabola with top is given: .

Seems straightforward enough and when try to solve this, for example, for , I just fill in the blanks and solve for a: this sure enough works out as I would've expected.

But then I'm asked to solve for the following: . Filling in tells me: Leaving me to conclude that , which according to my textbook is very wrong, it should be: .

Obviously I'm doing this wrong, so I'm looking for some pointers on how to approach a problem like this.

*As English isn't my native language it's possible I confuse terms, in spite of trying to find a fitting translation. I apologise for that on beforehand and hope you would be able to correct me if I do so.