Find Expression for Cubic Function: f(1)=6, f(-1)=0, f(0)=f(2)=0

  • Thread starter Thread starter DrDanger
  • Start date Start date
  • Tags Tags
    Expressions
Click For Summary

Homework Help Overview

The discussion revolves around finding an expression for a cubic function given specific values at certain points: f(1)=6, f(-1)=0, f(0)=0, and f(2)=0. The subject area is polynomial functions, specifically cubic functions and their properties.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the zeros of the function and its factors. There are attempts to identify the factors corresponding to the known zeros, and questions arise about how to express these factors correctly.

Discussion Status

The discussion is ongoing, with participants exploring how to express the cubic function based on its roots. Some guidance has been offered regarding the formulation of factors, but there is no explicit consensus on the complete expression for the function yet.

Contextual Notes

Participants are navigating the constraints of the problem, including the requirement to find a cubic function that meets the specified conditions without additional information on the function's form.

DrDanger
Messages
44
Reaction score
0

Homework Statement



Find an expression for a cubic function (f) if f(1)=6 and f(-1)=f(0)=f(2)=0

Homework Equations





The Attempt at a Solution


I tried to graph the points and find an equation for the function, but couldn't.
 
Physics news on Phys.org
Do you know about the relationship between zeros of a function and its factors?
 
Bohrok said:
Do you know about the relationship between zeros of a function and its factors?

yeah the factors are the zeros, right?
 
Yes. You know what values of x make the function 0, so how do you write the zeros as factors?
 
Bohrok said:
Yes. You know what values of x make the function 0, so how do you write the zeros as factors?

(x+1)(x-2)?
 
DrDanger said:
(x+1)(x-2)?

You have two; what's the last one?
 
Bohrok said:
You have two; what's the last one?
(x+6) lol I have no idea! I know it involves f(1)=6 though
 
If your cubic function has a root at x = 0 ( because f(0) = 0), might you write the factor something like (x + 0)? How would you rewrite that factor and put it with the other two factors?
 

Similar threads

Derivative Problem: f’(1), f’(2), f’(3), and f’(5)
  • · Replies 11 ·
Replies
11
Views
2K
Differentiable function proof given ##f''(c) = 1##
  • · Replies 1 ·
Replies
1
Views
1K
Show uniqueness in Dirichlet problem in unit disk
  • · Replies 6 ·
Replies
6
Views
2K
How to write sin(n*pi/2) as an expression (-1)^f(n)?
  • · Replies 8 ·
Replies
8
Views
5K
Find f s. t. ||f||=1 and f(x) < 1 with ||x||=1
  • · Replies 20 ·
Replies
20
Views
3K
Proof given ##x < y < z## and a twice differentiable function
  • · Replies 8 ·
Replies
8
Views
2K
Non-Differentiable Function proof
  • · Replies 8 ·
Replies
8
Views
1K
Can this function still be a constant function?
  • · Replies 11 ·
Replies
11
Views
2K
Why is this valid? Continuity of Functions Problem
  • · Replies 3 ·
Replies
3
Views
1K
How should I show that ## B ## is given by the solution of this?
  • · Replies 2 ·
Replies
2
Views
1K