How to get Formula from a Cubic Graph

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Homework Help Overview

The discussion revolves around determining the formula of a cubic polynomial based on its graph. Participants are exploring how to identify the roots and coefficients of the polynomial from the visual representation of the function.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to identify the values of b, c, and d, which represent the roots of the polynomial where f(x)=0. There are questions about how to extract these values from the graph, as well as inquiries about determining the coefficient a.

Discussion Status

The discussion is ongoing, with some participants expressing confusion about the previous responses. There is a focus on interpreting the graph to find the necessary values for the polynomial equation, and some guidance has been offered regarding how to read the graph for these values.

Contextual Notes

There appears to be some frustration regarding the clarity of the responses, indicating a potential gap in understanding how to interpret the graph effectively. The original poster expresses a lack of direction in their attempts to solve the problem.

Jordash
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Homework Statement



The figure shows the graph of a cubic polynomial.

GraphFigure.png
The function graphed is f(x)=

Hint: You may write the function as f(x) = a(x-b)(x-c)(x-d) where b, c, and d, are integers and a is a fraction.

Homework Equations


The Attempt at a Solution



I'm lost...
 
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When f(x)=0 the graph cuts the x-axis, so what are the values of b,c and d?
 
b, c and d are where f(x)=0, can't you read those off from the graph? Now what about a?
 
I'm sorry but both of those answers made no sense...
 
Jordash said:
I'm sorry but both of those answers made no sense...

Are you unable to read the number off of the graph? Which part made no sense?
 
Simply by observing the graph you should be able to find b, c, and d in your equation f(x) = a(x -b)(x - c)(x - d).

And you should be able to get a by noticing where the graph crosses the y-axis.
 

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