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

Jun 27, 2015

$y = - 2 {\left(x + 5\right)}^{2} - 2$ is a continuous function with an infinite number of $\left(x , y\right)$ 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: $\left(- 5 , - 2\right)$

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 $y$
$y = - 2 {\left(0 + 5\right)}^{2} - 2 = - 52$
So the y-intercept occurs at $\left(0 , - 52\right)$