# Question #c0eb1

Aug 13, 2017

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 $\left(- 8 , - 2\right)$

The graph also appears to pass through the points:

$\left(- 7 , - 1\right)$, $\left(- 4 , 0\right)$, $\left(1 , 1\right)$, $\left(8 , 2\right)$

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 $\left(- 4 , 0\right)$.

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

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