Quadratic Function
Change the coefficients and the curve will obey
Summary
A parabola is the graph of a second-degree polynomial function: f(x) = ax² + bx + c. Move the a, b and c sliders to change, instantly, how wide the parabola opens, where it sits and where it crosses the y-axis.
In depth
Because a quadratic function contains an x² term, its graph takes the classic "U" shape called a parabola. The coefficient a sets how wide the parabola opens and in which direction: if a > 0 it opens upward, if a < 0 downward; the larger |a|, the narrower the parabola. The vertex is at x = −b/(2a). Whether the function has real roots (the points where the parabola crosses the x-axis) is decided by the discriminant Δ = b² − 4ac: if Δ > 0 there are two distinct real roots, if Δ = 0 a double root (the parabola touches the x-axis), and if Δ < 0 no real roots. All of this can be watched live in this interactive visualisation.
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