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

In summary, the conversation was about finding the equation for a cubic function using given x-intercepts and a y-intercept. After attempting to substitute the y-intercept and solving for the constant, the correct equation was found to be f(x)= 3.923(x+1.57)(x-0.65)(x-2.83). However, there was a mistake made in graphing the equation on a calculator.
  • #1
ShawnPrend
2
0

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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 

1. How do you find the equation of a cubic function?

To find the equation of a cubic function, you need to have three known points on the graph of the function. Plug in the x and y coordinates of each point into the general form of a cubic function, ax^3 + bx^2 + cx + d, and solve for the four coefficients a, b, c, and d.

2. What is the general form of a cubic function?

The general form of a cubic function is ax^3 + bx^2 + cx + d, where a, b, c, and d are constants that determine the shape and position of the graph. The leading coefficient, a, determines the steepness of the graph and whether it opens upwards or downwards.

3. How many real roots can a cubic function have?

A cubic function can have up to three real roots. However, it is possible for a cubic function to have less than three or even no real roots, depending on the coefficients a, b, c, and d in the general form of the function.

4. What is the relationship between the graph of a cubic function and its roots?

The roots of a cubic function are the x-intercepts of its graph, which are the points where the function crosses the x-axis. The number of roots a cubic function has is equal to the number of times its graph crosses the x-axis. This means that a cubic function with three real roots will intersect the x-axis in three distinct points.

5. Can a cubic function have complex roots?

Yes, a cubic function can have complex roots. If the coefficients a, b, c, and d in the general form of the function are complex numbers, then the roots of the function will also be complex numbers. However, if the coefficients are all real numbers, then the cubic function will have either three real roots or one real root and two complex conjugate roots.

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