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Science Design
Equations
Quadratic Formula, Parabola Roots and Discriminant

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Quadratic Formula, Parabola Roots and Discriminant

The quadratic formula, x = (-b +/- sqrt(b^2 - 4ac)) / 2a, gives the two roots of any equation ax^2 + bx + c = 0. Its method goes back to the ninth-century mathematician Muhammad ibn Musa al-Khwarizmi, whose work gave algebra its name. The design shows three parabolas sharing the same axis: one crossing the x-axis at two marked roots, one touching it once, one never reaching it, showing how the sign of the discriminant b^2 - 4ac decides how many real roots exist.

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