horizontal axis of symmetry through the point (7,11) would be y=11, with the vertex also having a y coordinate of 11.
but you've given the vertex as (-5,-7). The problem has contradictory information. and no solution
the problem is slightly ambiguous.
Unless it reads "horizontal axis of symmetry" and through the point (7,11) but not on the axis of symmetry.
a horizontal axis of symmetry means either a right or leftward opening parabola of the form x=a(y-h)^2 + k
where (h,k) is the vertex. plug in (-5,-7) for (h,k) and (7,11) for (x,y) to solve for "a"
7 =a(11+7)^2 -5
18=256a
a = 18/256 = 1/27
x=(1/27)(y+7)^2 - 5 might seem to be the solution, but if it assumes a line of symmetry inconsistent with the vertex there is no solution.
either the problem was copied with a typo, or the problem itself was in error. If the latter, then use the fake solution. It's what they expect.
Or if the point (7,11) was not intended to be on the axis of symmetry then x = (1/27)(y+7)^2 - 5 is the correct solution.
a>0 means it's a rightward opening parabola. (7,11) to the right of the vertex means rightward opening.
