Plot and analyze Quadratic, Cubic, and Quartic functions. Automatically calculates vertex and roots for parabolas.

Function Properties

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    How to Use

    Graphing Polynomials

    This tool allows you to visualize functions of higher degrees. While a linear equation ($y=mx+b$) produces a straight line, higher-order polynomials produce curves with peaks and valleys.

    Degrees Explained

    • Degree 1 (Linear): A straight line.
    • Degree 2 (Quadratic): A Parabola (U-shape). This calculator will automatically find the Vertex (the turning point) and the Roots (where it crosses the x-axis).
    • Degree 3 (Cubic): An S-shaped curve that can have up to two turning points.
    • Degree 4 (Quartic): A W-shaped or M-shaped curve with up to three turning points.

    The Math Behind It

    Standard Polynomial Form:

    $$ P(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0 $$

    Where:

    • $n$ is the Degree (highest power).
    • $a_n$ are the Coefficients (the numbers in front of the variables).