Question

What is the general equation of parabola whose axis of symmetry is parallel to y-axis?
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Answer 1

your question is nonsensical

Answer 2

y=ax^2 +b

Answer 3

y=ax^2 +bx+c which one

Answer 4

y=ax^2 +b

Answer 5

A parabola can have the axis parallel to the x-axis, even though the complete parabola does not make a function (because it does not pass the vertical line test).

The general formula for the parabola with a vertical axis is:
y=a(x-h)+k
where (h,k) is the vertex.
so the one with a horizontal axis is
x=a(y-k)+h
where (h,k) is still the vertex.