Question

A parábola has an axis of symmetry x = -2 and passes through the point (-5,6). Find another point that lies on the graph of the parabola

Answer 1

There will always be a point symmetrical to the given point on the other side of the parabola.
To find that other point, know that the perpendicular distance to the line of symmetry is the same for both points.
The perpendicular (shortest) distance from (-5,6) to the line x = -2 will be to the point (-2,6) on that line.
The perpendicular (shortest) distance from (-5,6) to the line (-2,6) is the change in x coordinates, or absolute value difference in x coordinates. |-5--2| = 3.
Then go 3 units to the right of (-2,6) to find the other point because the other symmetrical point also is the same distance to the middle point (-2,6). The answer is (1,6)