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Answer 1 · 2017-08-13T21:19:47

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

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

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

The graph also appears to pass through the points:

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

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

$1, 4, 9, 16$ $1, 4, 9, 16$

recognisable as the first four positive square numbers.

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

$y = \sqrt{x + 8} - 2$ $y = sqrt(x+8)-2$

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

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

$0 = \sqrt{x + 8} - 2$ $0 = sqrt(x+8)-2$