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(x)=x^2+6x+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#.

    Image by Maurizio Giaffredo

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

  • Answer:

    See the explanation section.


    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#.)