Use your equations from Lesson 1 for the Brick candle and the Egyptian candle to create a graph of two polynomial functions so that you can compare volumes for different values of x. Compare the volumes. My equations from lesson 1 were x^3-x^2 for the brick, and 7x^2 for the Egyptian.

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  the cubic does not exceed the quadratic until x > 8

Step-by-step explanation:

The attached graph plots the two expressions. The two are equal at x=8. Below that value the expression 7x^2 is greater. Above that value, the expression 7x^3 -x^2 is greater.

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Comment on the question

The directive to "compare the volumes" does not tell anything about the sort of comparison you are expecting. We note that the expression x^3-x^2 is zero or less up to the point where x=1, so we wonder exactly what it is supposed to be modeling. Any real volume will not be negative.

For small values of x, the quadratic is quite a bit larger. However, we know the cubic will grow larger than any quadratic for large values of x. So, the comparison you get will depend on the domain of interest—which is not specified.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.