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

1 Answer
Oct 16, 2015

Answer:

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(x)=ax^2+bx+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 #(h,k)# through the points #(h+-1,k+a)#,
(that is, it opens up or down)
the standard form is #y = a(x-h)^2 + k#

(If the parabola opens sideways, it includes the points #(h+a, k+-1)# and has form #x = a(y-k)^2+h#.)