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How would I do this problem if I decided to use x^3?
Help me please?
Need a polynomial a little more complex to explain this properly. Say for example: x^3+x^2-17x+15
Can you explain what the x-intercepts means to you?
they will be the points at which the line crosses the x-axis?
Thanks. So, how do we get the x intercepts?
It also means where Y equals zero, so these are the roots of the function.
Do you know how to find the roots of a function? By saying factoring?
set it to zero
so, 0 = x^3 + x^2 - 17x + 15?
That is the second step, first you need to simplify the polynomial. something like (ax+b) (cx^2+dx+e) This a difficult polynomial to determine the first root, so it you have a graphing calculator try to plot the equation.
It will look something like this. |dw:1449503213740:dw|
i agree. where do we go from here?
Part of my problem is that I don't know how to put together my answer.
I want to explain how to find the x intercepts, but I don't know how to do that and also I also want to explain how to construct a rough graph of R(x) so that the engineer can predict when there will be no change in the direction of the coaster.
If your interest the roots to the polynomial are -5, 1, and 3. 0 = (x-1)(x-3)(x+5)
I already told you how to find the x-intercept. Can you predict when the train change direction, from up to down or down to up.
CORRECTED ENTRY The QUESTION does NOT ask up how to find the roots, just what how to find the x-intercept (ie find the roots) and how does the engineer know when the coaster changes directions (form up to down or down to up). So what do you think about the second part of the question?
Oh okay thanks. so i would say to make y = 0 and then solve? for the second part, he knows when to change direction because of the positive and negative values of x?
No on both questions.
What do you propose?
You said earlier when asked about the x-intercept MathHelpPls they will be the points at which the line crosses the x-axis? What a these points of the polynomial called besides the x-intercepts? They are the ________ of the equation. (Fill in the blank)
Yes! So how would you answer the first question?
Upon graphing the equation, x^3 + x^2 - 17x + 15, you will see the points at which the line crosses the x-axis, making these points the x-intercepts of the graph. These points are the roots of the equation.
Is this right?
Extremely excellent answer!
Whew! now i'm getting somewhere! haha Now, for part 2, I don't understand what causes the graph to change, like go up and down.
are you still there? @retirEEd
Yes. I just had to really think about your question. The function causes the response of the graph.
How can the engineer predict when there will be NO change in the direction of the coaster?
I think i might just have to simply state exactly that. It doesn't say to explain why the graph changes direction or would not change. For my final answer, would saying this sound good?: Upon graphing the equation, x^3 + x^2 - 17x + 15, you will see the points at which the line crosses the x-axis, making these points the x-intercepts of the graph. These points are the roots of the equation. The function, x^3 + x^2 - 17x + 15, causes the graph to move up and down in a specific way unique to this function. But, it seems like i'm missing something.
i don't know how he will be able to.
Look at the drawing of the graph I inserted. What is the primary difference bewteen the lines AB and CD? |dw:1449506017315:dw|
they are going opposite directions. they are perpendicular to eachother
The first part is correct. They weren't meant to be perpendicular, but take doesn't matter and besides, that's not a difference, but an observation. Say they are perpendicular. What is unique about perpendicular lines?
perpendicular slopes have opposite signs. The other "opposite" thing with perpendicular slopes is that their values are reciprocals
Correct. So what if the lines weren't perpendicular, only the first part of answer would be true. What does that tell you about the graph of the polynomial?
If the lines weren't perpendicular, then the lines would be straight and therefore have the same signs?
So, the graph of the polynomial would have areas where the line wouldn't change because the points have the same sign in those areas?
You got it. I realize you are very smart and appear to be training or testing my tutoring skills. I appreciate that, since I am very new to this endeavor. But now it is time to take my dog for a walk. Have a good day!
Okay. Thank you for helping me. I appreciate that you spent this much time! You have helped a tremendous amount!