Vertex form of parabola; why x-h, not x+h?

Cicnar

Hello.

The vertex form is y= a(x-h)^2+k, in general. Could it also be defined as y= a(x+h)^2+k?
I am wondering about that minus sign. I see no particular use of it. Is it there because of tradition
or am i missing something?

lurflurf

The vertex of y= a(x-h)^2+k is (h,k)
The vertex of y= a(x+h)^2+k is (-h,k)

We need a minus somewhere.

johnqwertyful

When x=h, you have y=0+k=k
The vertex is h,k.

Cicnar

Thanks for your replies. But i think i was misunderstood. I will try to explain better this time.

For example, a general equation of a line is y=ax+b. What is special about addition operation? Is just a matter of convention? Could i say "a general equation of a line is given by y=ax-b"? I see nothing wrong with it.

Now, same logic for y= a(x-h)^2+k. This x-h part can be (or cant?) written as addition (x+h), if we choose to set our general equation in such form? Its a minor issue, but i was curios.

symbolipoint

The different forms of equations make certain things easier to know about them.
y=mx+b, and y=ax^2+bx+c are the GENERAL form of a line, and of a parabola. They are easy to use for finding y values, and more convenient if using matrices. Ax+By=C, and y=a(x-h)^2+k are the STANDARD form for a line and for a parabola. The number-line intercepts are easy to identify for the line, and the vertex is easy to identify for the parabola, from the standard forms.

Cicnar

Oh, i see now! We can read more easily the desired information in this particular form (in this example, that is the coordinates of vertex). Makes perfect sense why this is the standard form now.

Thank you very much, symbolipoint.