Standard Form of the Equation

Key Questions

• I believe you mean standard form. Standard form has another name, vertex form.

This is a duplicate question, please read the link below as it also has an example: How do I convert the equation $f \left(x\right) = {x}^{2} + 6 x + 5$ to vertex form?

• The directrix of the parabola is a straight line that, together with the focus (a point), is used in one of the most common definition of parabolas.
In fact, a parabola can be defined as *the locus of points $P$ such that the distance to the focus $F$ equals the distance to the directrix $d$.

The directrix has the property of being always perpendicular to the axis of symmetry of the parabola.

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 $x = a {\left(y - k\right)}^{2} + h$.)