Question

How do you solve `y=-2(x+5)^2-2`?

Answer 1

`y=-2(x+5)^2-2` is a continuous function with an infinite number of `(x,y)` pairs which could be considered solutions.
There is no "solution".

Explanation:

graph{-2(x+5)^2-2 [-14, 6, -9.08, 0.92]}

We could find the solutions for a couple of points that are often of interest.

The equation itself is in the "vertex form" and we can read the coordinates of the vertex directly from the equation: `(-5,-2)`

The line represented by this equation does not touch the x-axis,
so there is no x-intercept.

However, we can determine the coordinates of the y-intercept by setting `x=0` in the equation and solving for `y`
`y = -2(0+5)^2-2 = -52`
So the y-intercept occurs at `(0,-52)`