Question

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

Answer 1

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`.)