# What is the standard form of the equation for a parabola?

Oct 16, 2015

See the explanation section.

#### Explanation:

The term "standard form" is perhaps overused in mathematics.

The standard form for a quadratics function (as a polynomial function) is $f \left(x\right) = a {x}^{2} + b x + c$.

The standard for for the equation of a parabola (also called the vertex form) is like the standard form for other conic sections.

For a parabola with vertex $\left(h , k\right)$ through the points $\left(h \pm 1 , k + a\right)$,
(that is, it opens up or down)
the standard form is $y = a {\left(x - h\right)}^{2} + k$

(If the parabola opens sideways, it includes the points $\left(h + a , k \pm 1\right)$ and has form $x = a {\left(y - k\right)}^{2} + h$.)