Two quadratic polynomials f(x) and g(x) share the zeros −1 and 3.
(i) Write the simplest monic quadratic polynomial that has these zeros.
(ii) If f(x) passes through the point (0,−4), determine an explicit expression for f(x).
(iii) The polynomial g(x) has its minimum value −10 at x=1. Determine an explicit expression for g(x).
(iv) State the sign of the leading coefficient of each polynomial obtained in parts (ii) and (iii) and hence describe whether the corresponding graphs open upward or downward.
(v) Calculate the vertical distance between the vertices of the two parabolas.