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

In summary, the conversation discusses the vertex form of equations and whether it can also be written with a positive sign instead of a negative sign. The purpose of the minus sign is for tradition and convenience in identifying certain information. The standard form is more convenient for identifying important points such as the vertex.
  • #1
Cicnar
14
0
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?
 
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  • #2
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.
 
  • #3
Cicnar said:
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?

When x=h, you have y=0+k=k
The vertex is h,k.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 

1. What is the vertex form of a parabola?

The vertex form of a parabola is y = a(x-h)^2 + k, where (h,k) represents the coordinates of the vertex and a is a constant that determines the shape and direction of the parabola.

2. Why is the variable x subtracted by h in the vertex form?

The variable x is subtracted by h in the vertex form because it allows us to easily identify the coordinates of the vertex as (h,k). This form also makes it easier to graph the parabola as the vertex is located at (h,k) and the parabola opens either up or down depending on the value of a.

3. Can x+h be used in the vertex form instead of x-h?

Yes, x+h can also be used in the vertex form, but it is more common to use x-h. This is because when x is subtracted by h, it is easier to identify the coordinates of the vertex as (h,k) and it is also consistent with the standard form of a parabola, y = ax^2 + bx + c, where h is equal to -b/2a.

4. What is the significance of the h value in the vertex form?

The h value in the vertex form represents the horizontal shift of the parabola. If h is positive, the parabola will shift h units to the right, and if h is negative, the parabola will shift h units to the left. This value is important in determining the position of the vertex and the shape of the parabola.

5. Is there a specific reason why h is always subtracted in the vertex form?

The reason why h is always subtracted in the vertex form is to maintain consistency with the standard form of a parabola, y = ax^2 + bx + c. In this form, the vertex is located at (-b/2a, c). By subtracting x by h in the vertex form, the coordinates of the vertex remain consistent and it is easier to graph the parabola.

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