x-intercepts

Question

Suppose that the graph of f(x) =ax^2+bx+c has x-intercepts (m, 0) and (n, 0). What are the x-intercepts of g(x) =-ax^2-bx-c?

Answer 1

In this case, g(x) = -f(x).  That means that g(x) is a reflection (mirror image) of f(x) about the x-axis.  Any points on the x-axis, then, are unchanged (since they reflect right onto themselves).  So the x-intercepts of g(x) are the same as those for f(x): (m,0) and (n,0).