Polynomial Graph Calculator

Understanding polynomial functions is fundamental in mathematics, science, and engineering. A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. The general form of a polynomial equation is often written as:

y = a_nxⁿ + a_n-1x^n-1 + ... + a₂x² + a₁x + a₀

Where:

y is the dependent variable (output).
x is the independent variable (input).
a_n, a_n-1, ..., a₀ are the coefficients (real numbers).
n is the degree of the polynomial (a non-negative integer).

This calculator helps you generate a series of (x, y) coordinates for a polynomial function up to the 4th degree. By inputting the coefficients for each term and defining a range for 'x' values, you can obtain the points necessary to plot the graph of the polynomial.

How to Use the Calculator:

Enter Coefficients: Input the numerical coefficients for each power of 'x' (x⁴, x³, x², x¹) and the constant term (x⁰). If a term is not present, enter '0' for its coefficient.
Define X Range: Specify the minimum and maximum 'x' values for which you want to calculate 'y' values.
Set X Step Size: Determine the increment for 'x' values. A smaller step size will generate more points, resulting in a smoother graph when plotted, but will also produce a longer list of coordinates.
Calculate: Click the "Generate Points" button to see the list of (x, y) coordinates.

Interpreting the Results:

The output will be a table of 'x' and 'y' values. Each row represents a point (x, y) on the graph of your polynomial function. You can use these points to manually plot the graph on a coordinate plane or input them into a graphing software to visualize the polynomial's shape, roots, turning points, and overall behavior.

Polynomial Equation: y = ax⁴ + bx³ + cx² + dx + e

Coefficient for x⁴ (a):

Coefficient for x³ (b):

Coefficient for x² (c):

Coefficient for x¹ (d):

Constant Term (e):

Minimum X Value:

Maximum X Value:

X Step Size:

Enter values and click 'Generate Points' to see the (x, y) coordinates.

Generated (x, y) Coordinates:

'; tableHTML += '

'; tableHTML += ''; tableHTML += ''; tableHTML += ''; for (var i = 0; i < points.length; i++) { tableHTML += ''; tableHTML += ''; tableHTML += ''; tableHTML += ''; } tableHTML += '

X Value	Y Value
' + points[i].x.toFixed(4) + '	' + points[i].y.toFixed(4) + '

'; resultDiv.innerHTML = tableHTML; }