 ## Tutoring on Determining the Equations of Polynomial Functions

Learning Objectives:

#### Understand to Determine the Equations of Polynomial Functions.

Math Tutoring on Determining the Equations of Polynomial Function

To find a possible equation for a polynomial function let us review what we know about the zeros of a polynomial function. First, the zeros or roots of a polynomial function are the x values for which f(x) = 0. If the zeros or roots are r₁, r₂ and so-on, this gives us information about factors of the polynomial function. If r₁ is a 0, then (x - r ₁) would have to be a factor of the function. If r₂ is a 0, then (x - r₂) would also be a factor of the polynomial function and so on. Then the possible polynomial function is f(x) = a(x - r₁)(x -  r₂)… ……, we will let a=1 unless r is a fraction. If the polynomial function has complex zeros or roots, they always come in conjugate pairs (a+bi) and (a-bi).Lastly, graphically, if we have real zeros, the real zeros would be the x intercepts of the graph of the function. The method for finding the equation is similar to that in a quadratic, but in the case of polynomials, we do not have a vertex point. In math tutoring, this is why we use the zeroes.

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Hook Questions:

1. What is a polynomial function?

2. What are zeros or roots of a polynomial function?

3. How to write the equation of a polynomial using x-intercept?

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