If we know that the function intersects the x-axis at x=5 and x=9, we know that this values (x=5 and x=9) are the roots of the quadratic function.
If we know that this are the roots of the quadratic function, we can express the family of functions that satisfies this condition as:
where C can be any real number.
In that equation we can see that g(x) = 0 when x=5 and x=9.
The only equation that belongs to this family is Option A, where:
Option B has roots in x=-5 and x-9, so it is not a candidate for g(x).
Option C has values for g(x) higher than 0, so it has no real roots. Then, it is not a candidate for g(x).
Option D have the same condition than option C.