When Algebra 1 students find the vertex of a parabola, they use x=-b/(2a).
When Geometry students find the mirror line of the reflection (x,y)–>(b-x,y) they get x=b/2.
So I thought, what if there’s a dilation-reflection composition (x,y)–>(b+ax, y) ? then the mirror line will exist at x=-b/(2a), right?
Not sure. Just noting this to come back and check when my grading is done.