Question

Plot the following parabolic functions in Excel and then answer the discussion question below . Use at least 8 points for each plot: Each graph is worth 15 points and must include 8 points. 1) y=x2-6x+8 2) y=x2+4 3) y=(-1/2)(x2) 4) What is the maximum number and the minimum number of x-intercepts for a parabola? Why? (15 points) In order to obtain full credit, you will need to plot the functions in Excel or using the Open Office feature and attach the results to your response.

Answer 1

1) Plot for

2) Plot for 3) Plot for

4)

For any given parabola maximum number of x-intercepts is 2 while minimum number of x-intercept is 0

As we can see in above graphs parabola is a graph where it has two opening going away from each other and it has a single point from where these two paths starts as shown below

Now if this entire parabola lies above or below the x-axis then there wont be any x-intercept hence minimum number will be 0 (as in question (2))

If the single point lies on the x-axis (as in question (3)) then there will be only 1 x-intercept

If the parabola cuts the x-axis such that the single point is not on x-axis then there will be two x-intercepts hence maximum is two