Determining the equation of a polynomial function

Determining the equation of a polynomial function

We can easily find the equation of a polynomial from its graph by identifying x-intercept and the sign of the leading coefficient. That way, we can determine the factors of the polynomial and the end behavior of the function.

Lessons

Steps to determining the equation of a polynomial function
1. Find the zeros, write them out in factored form.
2. Determine the multiplicity each zero by observing the behavior of the graph near the zero.
3. Determine the leading coefficient C by plugging in the coordinates of a point (other than the x-intercepts) on the graph.
  • Introduction
    Steps to Finding the Equation of a Polynomial Function
  • 1.
    Determining the Equation of a Polynomial Function With Multiplicities Equal to 1
    Determine the equation of the polynomial function of lowest possible degree in factored form.
    a)
    Determining the equation of a polynomial function from the graph

    b)
    Determining the equation of a polynomial function of the lowest degree

  • 2.
    Determining the Equation of a Polynomial Function With Higher Multiplicities
    Determine the equation of the polynomial function of lowest possible degree in factored form.
    Determining the equation of a polynomial function
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3.
Polynomial Functions
3.1
What is a polynomial function?
3.2
Polynomial long division
3.3
Polynomial synthetic division
3.4
Remainder theorem
3.5
Factor theorem
3.6
Rational zero theorem
3.7
Characteristics of polynomial graphs
3.8
Multiplicities of polynomials
3.9
Imaginary zeros of polynomials
3.10
Determining the equation of a polynomial function
3.11
Applications of polynomial functions
3.12
Solving polynomial inequalities
3.13
Fundamental theorem of algebra
3.14
Descartes' rule of signs
Grade 12 Math