Question

Question #cdfa9

Answer 1

See explanation.

Explanation:

To verify algebraicly if a point lies on a parabola (or any other graph of a function) you have to substitute `x` and `y` in the function's formula with the point's coordinates.

Example 1

Let the function be `f(x)=(2x)/(x-1)` and the point `A=(2,4)`.

If we substitute the point's coordinates we get:

`4=(2*2)/(2-1)`

`4=4`

Both sides of the equality are the same, so the point lies on the graph.

Example 2

Let `f(x)=(x^2-4)/(x^2+4)` and the point `A=(0,3)`

Here we get:

`3=(0^2-4)/(0^2+4)`

`3=(-4)/4`

`3=-1`

The last equality is false, so the point `(0,3)` does not lie on the graph of the given function.

Note: This method works for all functions, I used rational functions, but there is no restriction on function's formula.