Question

Explain why you cannot use the axes of symmetry to distinguish between the quadratic functions

Answer 1

That is because there are many quadratic functions that have the same axis of symmetry.  If a function is multiplied by a constant factor the axis of symmetry remains the same but the curved part of  the graph widens or narrows.

For example  x^2 + x - 6  and 2x^2 + 2x - 12  The last function will have same axis of symmetry and same roots as the first but the curved part will be narrower.

Also if we multiply the first function by -1 the curve will flip about the x axis but will have the same axis of symmetry