Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a, b,c are all real numbers

(a) Derive an equation for a line tangent to both of these parabolas (show all steps, assuming that such a line exists)

(b) Assume that the doubly-tangent line has an equation y+Ax+B. Find an example of values of a, b,c (other than the ones given here or in class) such that A, B ∈ Z

(c) Consider the case a = 1. Does your algebra accurately reflect what we can expect geometrically? Explain.