Multiple Questions — Evaluating the graph of this polynomial

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Homework Help Overview

The discussion revolves around evaluating the graph of a polynomial, with participants exploring various aspects of the problem, including roots and function values. The original poster expresses difficulty with certain parts of the problem, particularly in relation to the graph and population proportions.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants inquire about the meaning of "root" in the context of the polynomial and how to find where the function equals zero on the graph. There are attempts to clarify the relationship between different parts of the problem, particularly how the answer to one part may inform another.

Discussion Status

The discussion is active, with participants asking clarifying questions and offering guidance on how to approach the problem. There is a focus on determining specific values and understanding the implications of those values in relation to the polynomial's graph.

Contextual Notes

Some participants express confusion about the steps involved, particularly regarding the calculation of certain coefficients and the use of specific points on the graph. There is an acknowledgment of the need to clarify definitions and relationships within the problem.

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Homework Statement
So essentially I have a math test tomorrow and I was out sick for the past week and now I am unable to really understand what is going on in the attached screenshots. I am attempting the first one yet I keep getting the incorrect answer. Any assistance to any of the questions would be much appreciated!
Relevant Equations
N/A
872861D0-2EB2-40FB-88F1-DEF117D8BD12.jpeg
E79701CF-5A1F-44EC-A146-EB1E4F696DA1.jpeg

61E8B8E3-17BC-494B-B4EA-8059F4F4CC2C.jpeg
5D1C5E65-C730-4A25-AAC4-CE17F281CAC1.jpeg
 
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What have you tried so far that gives you the wrong answer?
 
Office_Shredder said:
What have you tried so far that gives you the wrong answer?
For the graph one I genuinely have no idea. I actually was able to solve the one with the form and factor however I remain stuck on the proportion of population and graph problems.
 
You said you kept trying the first one and getting the wrong answer. What wrong answer did you get? How did you get it?

If you haven't been able to make any progress, maybe let's just start with the first part then. What does the word "root" mean there?
 
Office_Shredder said:
You said you kept trying the first one and getting the wrong answer. What wrong answer did you get? How did you get it?

If you haven't been able to make any progress, maybe let's just start with the first part then. What does the word "root" mean there?
Would the root be where the function is equal to zero?
 
So how do you find where the function is equal to zero on the graph?
 
It would be 2,5. Sorry I just realized how slow my brain is functioning right now.
 
How do you do the next part then?
 
Office_Shredder said:
How do you do the next part then?
Alright I was able to get (II) but I don’t know how to get (iii)
 
  • #10
The answer to ii is used to get iii, so why don't you tell us what you got?
 
  • #11
Office_Shredder said:
The answer to ii is used to get iii, so why don't you tell us what you got?
I got f(x)=p(x-2)(x-5)^2
 
  • #12
So can you expand that to figure out what a, b, c and d are? The only thing you need to do is figure out what p is. There's one point on the graph you haven't used yet that you can use to figure out p.
 
  • #13
Office_Shredder said:
So can you expand that to figure out what a, b, c and d are? The only thing you need to do is figure out what p is. There's one point on the graph you haven't used yet that you can use to figure out p.
Would that be (3,8)? Sorry but could you explain how I can figure out p and expand? I’m sorry I am just pretty confused.
 
  • #14
I guess let's start by figuring out p. Yes, try plugging in (3,8) and see what it gives you
 
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