Learning Objectives:

__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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