How To Find A Maximum Value For A Polynomial

Polynomials are used to represent functions that are not straight lines by including variables raised to exponents, such as x^2. These functions can be used to project or show a variety of data, including profit versus number of employees, letter grades versus number of students getting each grade and population versus resources. Finding the maximum of a polynomial helps you to determine the most efficient point. For example, if you were using a polynomial to predict the profit versus the number of employees, the maximum would tell you how many employees to hire and what your profit would be at that point.

Step 1

Arrange the polynomial into the following from: ax^2 + bx + c where a, b and c are numbers. For example, if you had 5 + 12x – 3x^2, you would rearrange it to read -3x^2 + 12x + 5.

Step 2

Determine whether a, the coefficient of the x^2 term, is positive or negative. If the term is positive, the maximum value will be infinity because the value will continue to grow as x increases. If it is negative, continue to step 2.

Step 3

Use the formula -b/(2a) to find the x-value for the maximum. For example, if your polynomial was -3x^2 + 12x + 5, you would use -3 for a and 12 for b and get 2.

Step 4

Plug the x-value found in step 3 into the original polynomial to calculate the maximum value of the polynomial. For example, if you plugged in 2 into -3x^2 + 12x + 5, you would get 17.