Finding the Equation of a Polynomial Function

How to find the Equation of a Polynomial Function?
Once we know the basics of graphing polynomial functions, we can easily find the equation of a polynomial function given its graph. To find polynomial equations from a graph, we first identify the x-intercepts so that we can determine the factors of the polynomial function. We can also identify the sign of the leading coefficient by observing the end behavior of the function.

How we identify the equation of a polynomial function when we are given the intercepts of its graph?
How to Find the Equations of a Polynomial Function from its Graph - Precalculus Tips.

Example:
Find an equation of the polynomial function f(x) for the graph shown.

Step-by-step directions on how to find the equation of the graph of a polynomial function

Example:
Write the equation of the graphed polynomial function in factored form. Find the exact value of the leading coefficient.

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How to find the Formula for a Polynomial given Zeros/Roots, Degree, and One Point?
If you know the roots of a polynomial, its degree and one point that the polynomial goes through, you can sometimes find the equation of the polynomial.

Example:
Find the polynomial f(x) of degree 3 with zeros: x = -1, x = 2, x = 4 and f(1) = 8

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Finding the Formula for a Polynomial Given: Zeros/Roots, Degree, and One Point - Example 2
If you know the roots of a polynomial, its degree and one point that the polynomial goes through, you can sometimes find the equation of the polynomial.

Example:
Write an expression for a polynomial f(x) of degree 3 and zeros x = 2 and x = -2, a leading coefficient of 1, and f(-4) = 30

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Finding the Formula for a Polynomial Given: Zeros/Roots, Degree, and One Point - Example 3.
If you know the roots of a polynomial, its degree and one point that the polynomial goes through, you can sometimes find the equation of the polynomial.

Example:
Find a polynomial, f(x) such that f(x) has three roots, where two of these roots are x =1 and x = -2, the leading coefficient is -1, and f(3) = 48. Assume f(x) has degree 3.

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Find an Equation of a Degree 4 Polynomial Function From the Graph of the Function
How to determine an equation of a polynomial function from the graph of the function?

Example:
Find an equation for the graph of the degree 4 polynomial function. Leave the function in factored form.

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Find an Equation of a Degree 5 Polynomial Function From the Graph of the Function

Example:
Find an equation for the graph of the degree 5 polynomial function. Leave the function in factored form.

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Determine Polynomial from its Graph
How to determine the equation of a polynomial from its graph. This includes taking into consideration the y-intercept.

Example:
y = -(x + 4)(x - 1)² + C
Determine the value of the constant.

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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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