What is the estimated cubic function for given x and y-intercepts?

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    Cubic Function
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The discussion focuses on deriving an estimated cubic function from given x-intercepts at (-1.57, 0), (0.65, 0), and (2.83, 0), and a y-intercept of 11.33. An attempt was made to calculate the function using the y-intercept, leading to the constant K being determined as approximately 3.923. The resulting function, f(x) = 3.923(x + 1.57)(x - 0.65)(x - 2.83), correctly satisfies all intercept conditions. A misunderstanding occurred when graphing the function, leading to confusion about its accuracy. Ultimately, the function meets all specified requirements for a cubic equation.
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Homework Statement



X-intercepts: (-1.57,0) , (0.65, 0) , (2.83, 0)
Y-intercept: 11.33



Homework Equations



I've got to convert that information into an estimated cubic function.


The Attempt at a Solution



I tried subbing the y-intercept in; although that didn't work.

11.33 = K(1.57)(-0.65)(-2.83)
11.33 = K(2.888)
K = 3.923

That didn't provide the correct equation when subbed into

f(x)=K(x+1.57)(x-0.65)(x-2.83)

Can anyone help me on this?
 
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I checked your solution process and tried your results. No problem found. You only have four points to use and to check. They all work in your function which you found.
 
Why do you say "that didn't provide the correct equation"?

Certainly f(x)= 3.923(x+ 1.57)(x- 0.65)(x- 2.83) is 0 at x= -1.57, x= 0.65, and x= 2.83 and, as you calculated f(0)= 3.923(.157)(-0.65)(2.83)= 11.33. It's a cubic and it satisfies all the requirements.
 
It was my own fault; I mixed up a few things when I was graphing the equation on a graphing calculator.

Thanks for the help though.
 
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