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More PreCalculus Lessons

These lessons, with videos, examples and step-by-step solutions, help PreCalculus students learn how to find 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.

**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

**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

**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.

**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.

**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.

**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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