find the vertex and the x-intercepts (If any) of the parabola. (If an answer does not exist, enter DNE) f (x) = 3x2-8x-3

The sketch shows a circle, a parabola, which is the graph of f, and a straight line, which is the graph of g. The parabola has zintercepts -2 and 6, and y-intercept 6. Its turning point is C. The circle has its centre at the origin and it passes through the point A, which has coordinates (-2,0). At point B both the circle and the straight line cut the z-axis. The straight line has y-intercept 1. 0 B Find the equation that defines f. Show that C has coordinates (2,8). What is the distance between A and C? Find the midpoint D of AC: Write down the equation of the circle that has AC as diameter. Find the maximum vertical distance between the graphs of f and g on the interval a [0, 6].

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