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


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.

Citation Info

  • [MLA] “quadratic.” Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 27 Mar 2013. Web. 27 Mar 2013. <>
  • [APA] quadratic (27 Mar 2013). Retrieved 27 Mar 2013 from the Platonic Realms Interactive Mathematics Encyclopedia:


Get the ultimate math study-guide Math & Me: Embracing Successproduct thumbnail image Available in the Math Store
detail from Escher pic Belvedere

Are you a mathematical artist?

Platonic Realms is preparing an online gallery space to showcase and market the works of painters, sculptors, and other artists working in a tangible medium.

If your work celebrates mathematical themes we want to hear from you!

Please let us know about yourself using the contact page.