2. Consider the graph of f (x) =x2 + 8x+18 a. Graph f(x) in detail in the xy plane of the coordinate system provided on the next page without using a graphing calculator. b. What conclusion can you make about the roots of f (x)? c. Show that -4+ 2i is a root for f (x). 12 ) = 1 - 4+7 21) 01- 4 + 2716 16- 4+27 - 412. . d. Show that f (-4-31) is a real number. e. Show that f (3+ 2i) is not a real number. f. Try a few more complex values and make a conjecture about values of a and b for which f (a + bi) is a real number. Explain how you arrived at your conjecture and prove that it is true. g. Lastly, draw a graphical representation of what your above answer imply about the real-valued outputs of f with regard to the inclusion of a complex domain. y X