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Question 1043155: "I'm thinking of creating three layers: two that have the same general shape and are based on the same equation, and one that is just a smooth curve in the background. I just need to decide how many bumps I want each curve to have, and how high they should be. We can adjust the height or location of each hill using a simple type of transformation.
If I want the background to have three hills, then I need a polynomial with three zeros. Maybe like this."
1. Here are the requirements for the layers of hills that teen 1 wants to create: two layers that have the same general shape — three hills — and are based on the same equation, and one layer that is just a smooth curve in the background.
Take a look at teen 1's initial polynomials for three layers of hills. Teen 1 has described what he thinks each modification to the initial polynomial will do. Sketch each curve (in a different color, preferably). (You will be asked to find and repair mistakes in the next section.) (6 points: 2 points for each curve)
Hill 1: My first layer needs three peaks. I chose three points on the x-axis
(the three zeros), and then I wrote each as a binomial to create the first polynomial. F(x) = (x – 1)(x – 3)(x – 4)
Hill 2: My second layer should be a useful transformation of the first. Using the first polynomial as the base, I multiplied it by to flip it and make the hills steeper. Then, I added 3 to shift it to the right. F(x) =– (x – 1)(x – 3)(x – 4) + 3
Hill 3: This hill should be a shallow parabola that will rise up in the foreground of my picture. F(x) = 4(x–)(x – 5)
2. Are these the hills teen 1 was trying to design? Remember, teen 1 wanted one layer of three hills, another set of three hills using the same base equation, and one long, low hill. Find any mistakes that teen 1 made in his design and in the reasoning he presented when explaining the transformations of the equations.
3. Write equations for three hills that do meet the requirements. Sketch them on one axis. (For the purposes of this exercise, this is a sketch, so the steepness and minimums and maximums of the graphs do not need to be exact).
4. What might be an advantage and a disadvantage of describing hills for a computer program using polynomial functions?
Answer by ikleyn(52800)   (Show Source):
You can put this solution on YOUR website! .
In our days, the average person is not able to read so long text.
It is very simple and very basic level truth (like axiom), which should be known to everybody . . .
Every and each reasonable school problem should be expressed in 3 - 4 - 5 lines.
Otherwise it is something different (probably, a story to read before sleeping) and, if presented as a problem,
is very likelihood candidate to the TRASH section.
Every reasonable thought/problem can be expressed in 3-4-5 lines.
You are always welcome in this WEB-site.
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