Question

Question #c0eb1

Answer 1

The function appears to be `y = sqrt(x+8)-2`, which is zero when `x=-4`.

Explanation:

This looks like the graph of the upper half of a parabola with horizontal axis.

The vertex is at `(-8, -2)`

The graph also appears to pass through the points:

`(-7, -1)`, `(-4, 0)`, `(1, 1)`, `(8, 2)`

If we add `8` to the `x` coordinates, they follow the pattern:

`1, 4, 9, 16`

recognisable as the first four positive square numbers.

So it appears that the formula of the curve may be written:

`y = sqrt(x+8)-2`

This function intercepts the `x` axis where `y=0`, i.e. at `(-4, 0)`.

So `x=-4` is the zero of the function and the root of the equation:

`0 = sqrt(x+8)-2`