Question

Which function is graphed below?

Answer 1

The function graphed below is
`x = y^(2) - 2` or
`y = \pm √(x+2)`.

Explanation:

The graph represents a second order polynomial function (a parabola), whose axis of symmetry is the x-axis and whose form is presented as follows:

`x - h = C\cdot (y-k)^(2)`

Where:

`x`,
`y` - Dependent and independent variable, dimensionless.

`h`,
`k` - Horizontal and vertical components of the vertex, dimensionless.

`C` - Vertex constant, dimensionless. If
`C > 0`, then vertex is an absolute minimum, otherwise it is an absolute maximum.

After a quick observation, the following conclusions are done:

1) Vertex is an absolute minimum (
`C > 0`) and located at (-2, 0).

2) Parabola pass through (2, 2).

Then, the value of the vertex constant is obtained after replacing all known values on expression prior algebraic handling: (
`x = 2`,
`y = 2`,
`h = -2`,
`k = 0`)

`2+2 = C\cdot (2-0)^(2)`

`4 = 4\cdot C`

`C = 1`

The function is:

`x = -2 + 1\cdot y^(2)`

`x = y^(2)-2`

The inverse function of this expression is
`y = \pm √(x+2)`

The function graphed below is
`x = y^(2) - 2` or
`y = \pm √(x+2)`.