How to get Formula from a Cubic Graph

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To derive the formula from a cubic graph, identify the x-intercepts where the graph crosses the x-axis, which correspond to the values of b, c, and d in the equation f(x) = a(x - b)(x - c)(x - d). The y-intercept, where the graph crosses the y-axis, helps determine the value of a. Observing these key points on the graph is essential for constructing the polynomial. If the graph's features are unclear, it may hinder the ability to extract these values accurately. Accurate reading of the graph is crucial for solving the problem effectively.
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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.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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