Problema Solution
Given the function f(x)=x(x-2)^2(x-4)
Find the x- and y-intercepts;
Determine whether the graph crosses or touches the x-axis at each intercept;
Graph the function
Please show all of your work. Submit your graph to the Dropbox
Answer provided by our tutors
the y-intercept occus when x = 0
so the y-intercept is at
y = 0(0-2)2(0-4)
y = 0(4)(4)
= 0
so the y-inercept is (0,0)
the x-intercepts occur when y = 0
0 = x(x-2)2(x-4)
x = 0
or (x-2)2=0
x-2 = 0
x = 2
or x-4 = 0
x = 4
so the x-intercepts are (0,0), (0,2), and (0,4)
in each part of the term, the graph crosses the x-axis if it came from something to an odd power and touches the x-axis if it came from something with an even power
so the graph crosses the x-axis at (0,0) and (0,4) since they came from x and x-4
the graph touches the x-acis at (0,2) since it came from (x-2)2
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