Answer to Tutorials on Quadratic Functions

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 ax2 + 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 ax2 gives the parabolic shape.



Interactive Tutorial (3)
Question:
a) f(x) = x2 + x - 2
b) g(x) = 4x2 + x + 1
c) h(x) = x2 - 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 b2 - 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 b2 - 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 b2 - 4ac > 0. How many x-intercepts the graph of f(x) has ?

Answer:
a)If b2 - 4ac < 0 there are no x intercepts.
b)If b2 - 4ac = 0 there is one x intercepts (graph touches x axis).
c) If b2 - 4ac > 0 there are two x intercepts.


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