Given f(x) = ex2 + fx + g, where e, f, and g are real numbers,
(a) Find the zeros of the function in terms of e, f, and g.
(b) Under what condition would the zeros of the given function be two distinct real values?
(c) Determine the x-coordinate (the x-value) of the point that would represent the minimum or the maximum of the graph of the function by taking the average (mean value) of the zeros of the function found in Part (a).
(d) Under what condition would the graph of the function have a maximum, not a minimum, with the x-value obtained in Part (c)?
(e) Draw the graph of a function, with numerical coefficients of your choice, to represent your thought on what you stated in Part (d).