A test program for grade 10 can generate quadratic functions in a standard form y = ax + bx + c where a, b, c are randomly selected from the following sets: a = {- 1,1, 2), b = {0, 4), c = {0. – 1} %3! C 3D a) Construct a tree diagram and show all possible quadratic functions generated by this program. b) How many of the functions in part (a) have a maximum value (i.e., downward opening)? c) What is the probability that a quadratic function randomly generated by this program has - a minimum value? - has 2 x-intercepts? - has a minimum and two real x-intercepts? - has no x-intercepts given it has a maximum?

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