Answers to the interactive tutorials on Quadratic functions are presented.

Interactive Tutorial (1)

Question: Set a to zero and explain the graph obtained. Which term in ax^{2} + bx + c gives the parabolic shape? Answer: If a = 0, f(x) = bx + c, the graph of f(x) in this case is a line: linear function.( if b = 0, f is a constant function). The term ax^{2} gives the parabolic shape.

Interactive Tutorial (3) Question: a) f(x) = x^{2} + x - 2 b) g(x) = 4x^{2} + x + 1 c) h(x) = x^{2} - 4x + 4 Use the analytical method described in the example to find the x intercepts and compare the results. Answer: a) The graph of f(x) has x intercepts are at (-2 , 0) and (1 , 0). b) The graph of g(x) has no x intercepts. c) The graph of h(x) has an x intercept (graph touches the x axis) at (-2 , 0). Question: a) Use the applet window and set a,b and c to values such that b^{2} - 4ac < 0. How many x-intercepts the graph of f(x) has ? b) Use the applet window and set a,b and c to values such that b^{2} - 4ac = 0. How many x-intercepts the graph of f(x) has? c) Use the applet window and set a, b and c to values such that b^{2} - 4ac > 0. How many x-intercepts the graph of f(x) has ? Answer: a)If b^{2} - 4ac < 0 there are no x intercepts. b)If b^{2} - 4ac = 0 there is one x intercepts (graph touches x axis). c) If b^{2} - 4ac > 0 there are two x intercepts.

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