# Equation of a parabola

1. Sep 11, 2014

### kevinshen18

The general equation of a parabola is:
(y - y1) = A(x - x1)^2

A is the scaling factor
y1 is the y coordinate of a vertex/point on the parabola
x1 is the x coordinate of a vertex/point on the parabola

My two questions are:
1. Can (x,y) be any point on the graph ?
2. If so, then if x - x1 = 0 and y- y1 = 0 (if the difference between the points are 0) then does that mean the point (x,y) is on the parabola?

2. Sep 11, 2014

### HallsofIvy

Staff Emeritus
Yes, (x, y) refers to any point on the parabola.

Your question is a little confusing (or confused). Again, (x, y) can refer to any point on the parabola. "if x- x1= 0 and y- y1= 0" then x= x1 and y= y1 is a specific point on the parabola. In fact, it is the vertex of the parabola- the lowest point if A is positive, highest point if A is negative.

3. Sep 11, 2014

### SteamKing

Staff Emeritus
That's what the equations of these curves are for.

Instead of having to compile a list of the infinite number of point coordinates which fall on the curve, a simple equation can be used to generate one point or many points, all of which will fall on the curve

Any point (x,y) which satisfies the equation of the parabola is a point on that parabola.

Now, why all of this confusion?

4. Sep 11, 2014

### Integral

Staff Emeritus
I would say that (x,y) is some point in the x,y plane, may on the parabola maybe not.

Points on a parabola are given by: (x, (x-x1)2+ y1))

5. Sep 12, 2014

### HallsofIvy

Staff Emeritus
In the original post the reference was to (x, y) satisfying the equation $(y- y_1)= A(x- x_1)^2$.

Those (x, y) are points on the parabola, not arbitrary points in the plane.

6. Sep 12, 2014

### kevinshen18

Thanks guys. So if (x,y) = (x1,y1), then this satisfies the parabola equation and (x1,y1) is the vertex?