(a) Find the zeros of each quadratic function g(x).
(i) g(x) = x2 − 4x − 12
(ii) g(x) = x2 + 5x
(iii) g(x) = x2 + 3x − 10
(iv) g(x) = x2 − 4x + 4
(v) g(x) = x2 − 2x − 6
(vi) g(x) = x2 + 3x + 4
(b) For each function in part (a), use a graphing utility to graph f(x) = (x − 2) ( g(x). Verify that (2, 0) is an x-intercept of the graph of f(x). Describe any similarities or differences in the behaviors of the six functions at this x-intercept.
(c) For each function in part (b), use the graph of f (x) to approximate the other x-intercepts of the graph.
(d) Describe the connections that you find among the results of parts (a), (b), and (c)?