If given the equation x = -1/8(y + 6)^2 + 2 what is the location of the focus point

Focus is at .

Step-by-step explanation:

Given:

The equation of the parabola is:

The standard form of a parabola in vertex form is given as:

Where, is the vertex of parabola. The value of decides the nature of parabola.

If , the parabola opens rightwards and if , the parabola opens leftwards.

Let us first rewrite the given equation in standard form.

On comparing the above equation with the standard one, we get,

Therefore, the focus of a parabola of the form is given by the point .

∴ Focus is

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step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)