Question

How do i determine the equation of a graph like this:

Answer 1

It looks like a parabola, with a given focal point.

Answer 2

@XxINFINITYxX
what do you think?

Answer 3

yep i was just wondering how the equation might be found for this, what is the process to do so?

Answer 4

Identify the coordinates of three points:
1. focus F,
2. vertex V
3. any other (convenient) point on the curve.

Answer 5

use directrix also..

Answer 6

Thanks @ganeshie8
I overlooked the directrix.
In that case, you would identify
1. focus F,
2. vertex V
3. equation of the directrix (dotted line below the x-axis)

Answer 7

Vertex is the "tip" of the curve, also the minimum (or maximum) of a parabola.

Answer 8

ok so in this case the vertex is the bottom of the curve and the focus is the single point above it?

Answer 9

Exactly.
The equation of the parabola is given by
\(y-k=(x-h)^2/4c\)
where V(h,k),
c is the distance between F and V.
c is also the distance between V and the directrix.
Must check that these two distances are equal.

Answer 10

ok so the distance between f and v, and v and the directrix will not always be the same? and what if they are not?

Answer 11

They should \(always\) be the same. If not, it may not be a parabola, or there is a mistake in the coordinates.

Answer 12

ok, so would the equation apply to a graph that was not a parabola such as this?

Answer 13

Could be, or part of it, or some other curve.
It is more likely a mistake of calculation of coordinates. Not too many curves I know of has a focus and a directrix. The question does not say that it is a parabola, so it is your job to make sure it is. One of the checks is the equality of the distance. Another check is that it is symmetrical about the vertical axis (through the focus). Third check is after finding the equation, check that all, at least some, points on the curve satisfy the equation.

Answer 14

ok ill check, thanks for the help

Answer 15

You're welcome! :)