quadratic

In general the term ‘quadratic’ refers to something involving a square, or the squaring of values, especially formulas or equations with squared terms.

Algebra/Calculus/Precalculus

A quadratic polynomial is a function of the form

\[p(x) = ax^2 + bx + c\]

where \(a\), \(b\), and \(c\) are real constants with \(a\neq 0\). The roots of a quadratic polynomial may always be found via the quadratic formula:

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

The expression under the radical is called the determinant. If the determinant is positive, both solutions are real; if negative, both solutions are complex; and if zero, there is a single solution of multiplicity two.

The graph of a quadratic is a parabola, and if the roots are real they correspond to intercepts of the parabola on the \(x\)-axis.