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

1 Answer
Jim H
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(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.)

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