Given 2 solutions, (-4,12) and (6,12), what is the axis of symmetry? How do you know? Explain your thinking mathematically.

1 answer

Poorly worded question.

The term "axis of symmetry" is usually associated with a parabola, so
I will assume you have two points on this parabola.
From the two equal values of y = 12, the axis of symmetry would be the
right bisector of the segment joining your two points,
that would be x = 1 , (notice the x of their midpoint is 1)

( the equation could be y = a(x-1)^2 + k
(6,12) lies on it, so 12 = a(25) + k
(-4,12) lies on it, so 12 = a(25) + k , same equation, so we don't have enough information to find a unique solution.

could be ....
let k = 11, 12 - 11 = a(25), a = 1/25
y = (1/25)(x-1)^2 + 11

let k = -13 , 12 = a(25) - 13 , a = 1
y = (x-1)^2 - 13

etc