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7 results for “quadratic”

Formulae (7)

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Finds the roots of any quadratic equation ax² + bx + c = 0.

\Delta = b^2 - 4ac

Determines the nature of the roots of a quadratic equation.

ax^2+bx+c = a\left(x+\frac{b}{2a}\right)^2 + c - \frac{b^2}{4a}

Rewrites a quadratic in vertex form.

x_1 + x_2 = -\frac{b}{a}, \quad x_1 x_2 = \frac{c}{a}

Relates the roots of a quadratic to its coefficients.

x^2 + bx = \left(x+\frac{b}{2}\right)^2 - \frac{b^2}{4}

Rewrite a quadratic as a perfect square plus a constant.

x = -\frac{b}{2a}

x-coordinate of the vertex of a quadratic.

O(n^2)

Runtime that grows with the square of input size.