If a vertical line passes through the supposed function at only one spot then you have a function.
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No, it does not. You can tell if something is a function or not by using the vertical line test. If there is more than one point at any vertical line, it is not a function.
Y = X2 ===== The graph of this parabola is crossed only at a point and once by a vertical line, so it is a function. Passes the vertical line test.
The given equation is not that of a parabola.
Standard notation for a quadratic function: y= ax2 + bx + c which forms a parabola, a is positive , minimum value (parabola opens upwards on an x-y graph) a is negative, maximum value (parabola opens downward) See related link.
It depends on where points h and k are, in which parabola. Since you have chosen not to share that information, there cannot be any sensible answer to this question.