Solve the following manually and SHOW the SOLUTION for each.

Do NOT use any graphing tools to answer the problems below.

A parabola and a circle may have 0, 1,2, 3 or 4 points of intersection. Sketch the circle x2 + y2 = 9 (label the center of the circle with your nickname). Discuss how this circle could intersect a parabola with an equation of the form y = x2 + k. Then find the values of k for each five cases described. a) No point of intersection b) One point of intersection c) Two points of intersection Three points of intersection Four points of interaction