Quadratic Function Range Calculator
Easily calculate the range of a quadratic function with our online calculator. Input coefficients a, b, and c to find the vertex and range instantly. Visualize the parabola graph.
Function Details
Enter the coefficients for the quadratic function in the form f(x) = ax² + bx + c.
Range:
Quadratic Function Visualization
Understanding Quadratic Function Range
A quadratic function is a polynomial function of degree two, generally represented as \(f(x) = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants and \(a \neq 0\). The graph of a quadratic function is a parabola. The range of a quadratic function is the set of all possible output values (y-values). For \(a > 0\), the parabola opens upwards, and the range is from the vertex's y-coordinate to positive infinity. For \(a < 0\), it opens downwards, and the range is from negative infinity to the vertex's y-coordinate. This calculator helps you find this range by calculating the vertex and determining the direction of the parabola.