how do you find the axis of symmetry given two pointssss without the midpoint formulaaa

The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

how do you find it given two points? you never explained that

Let the points be \((x_1,y_1)\;\;and\;\;(x_2,y_2) \)

The locus of all points equidistant from them will be the axis of symmetry.

\((x-x_1)^2+(y-y_1)^2=(x-x_2)^2+(y-y_2)^2\)

expand and simplfy that and you will have your axis of Symmetry.