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Answer 1 · 2017-08-13T21:19:47

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

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#