How to find the equation of a polynomial function from its graph?

We may make use of the various properties of polynomial curves and use it in finding the equation of the polynomial asked.

Answer: The solution of the equation of the polynomial is completed only by the detailed analysis of the graph values used to find the unknown values of the polynomial.

Two important observations from the graph include the x-intercept and the factors of the polynomial function which provide all information to deduce the equation of the polynomial.

Explanation:

To write an equation from the polynomial function's graph requires a step-by-step approach-

Step 1

We need to tabulate all the zeros of the graph which are nothing but the x-intercept of the graph.

Step 2

We need to assign a specific coefficient to each of the terms in the polynomial function. For ex - A quadratic equation has three terms, including a constant term, and is written as ax² + bx + c, where a, b is the coefficient, while c is the constant term. 

Step 3

The value of the coefficient is calculated by using the known values of f(x) at certain x-values taken from the graph and forming equations with coefficients as solutions to them.

Step 4

Finally satisfying all the zeros of the curve and hence, getting the desired result.

Hence, the solution of the equation of the polynomial is completed only by the detailed analysis of the graph values used to find the unknown values of the polynomial.