Let f(x)=3x2−8x+4. Answer the following:
a. Calculate the discriminant of f(x).
b. Using the result obtained in (i), state the number of x-intercepts of the graph of y=f(x) and mention whether the graph cuts or merely touches the x-axis.
c. Find the exact coordinates of all x-intercepts of the graph of y=f(x).
d. Sketch a rough graph of y=f(x), showing the direction of opening and clearly marking the intercepts found in (iii). (Scale is not required.)