As for subtracting the coefficients, what you are basically asking is whether ; of course not. You subtract exponents, and then only when the base is the same.

Swap the dependent and independent variables:

, so (assuming the inverse exists). Now solve for .

,not. Do your substitutions correctly.

Like the hint says, you can factor the numerator.

No. Complete the square and put the equation in standard form, , and the vertex will be at .

Now you should be able to find the vertex.

As I said, a parabola (with axis parallel to the -axis) with vertex at will have an equation of the form . So we have . Now substitute the second point in and solve for .

Beats me. We can't evaluate this without knowing .