Given the function f(x) = x(x+2)^2(x+4)

i. Find the x- and y-intercepts;
ii. Determine whether the graph crosses or touches the x-axis at each intercept;
iii. Graph the function

Please show all of your work.

Given the function f(x) = x(x+2)^2(x+4)

i. Find the x- and y-intercepts;
ii. Determine whether the graph crosses or touches the x-axis at each intercept;
iii. Graph the function

Please show all of your work.

@Mathematics

Question

Given the function f(x) = x(x+2)^2(x+4)

i. Find the x- and y-intercepts;
ii. Determine whether the graph crosses or touches the x-axis at each intercept;
iii. Graph the function

Please show all of your work.

Given the function f(x) = x(x+2)^2(x+4)

i. Find the x- and y-intercepts;
ii. Determine whether the graph crosses or touches the x-axis at each intercept;
iii. Graph the function

Please show all of your work.

@Mathematics

anonymous · Answer

The attached plot shows it all.

anonymous · Answer

How did you get this answer?

anonymous · Answer

This is a plot using the Mathematica 8.04 program.  The following line created the basic plot:
Plot [ x (x+2)^2(x+4), { x, -4.5, .5 } ]

anonymous · Answer

?

anonymous · Answer

"Plot [ x (x+2)^2(x+4), { x, -4.5, .5 } ]" had to be typed into a Mathematica "note book" followed by punching the "Enter" in the keypad portion of a full PC key board.  The plot then appears as part of a document.  Mathematica provides a procedure to save the plot as a PDF file.

anonymous · Answer

wow. yes i understand that sir. However, I am asking how you got to this answer. Is there a link I can connect to or do you have your work written out?

anonymous · Answer

A screen capture of a notebook portion is attached.

anonymous · Answer

I got this. I printed out the graph...my question is, can you show the work as to how you got this answer??

anonymous · Answer

The plotting portion of Mathematica did all of the plotting calculations automatically for x between x=-4.5 and x=0.5 

I had to tweak the plotting limits for x to make an enlargement of and center the area of interest.

anonymous · Answer

ok so what are these the x-intercepts? What are the y-intercepts? Its obvious the graph touches and crosses the x axis...correct?

anonymous · Answer

The x intercepts are where the graph crosses the x axis.  The plot shows x=-4 and x=0 are the two x intercepts.  There also is a y intercept at the point (0,0).

The graph touches, "is tangent to' the x axis at the point (-2,0).

You can also obtain the equation zeros from the equation itself.  In order for the equation to be zero, x can be -4, -2 or 0 from the equation factors.

anonymous · Answer

ok so i would put (-4,0)(0,0) for the first answer and then for the second answer I would put that yes it crosses and touches at -2. is that correct?

anonymous · Answer

Your answer looks OK except you might write that "it touches the x axis at (-2,0)"  Not sure how how much language hair splitting your teacher may engage in.

anonymous · Answer

ok- lol. I appreciate your help. It's hard to make this graph into an EZGraph that they want us to use...