# What is the the vertex of #x = (y -3)^2 - 9 #?

##### 1 Answer

The vertex coordinates are (3, -9).

#### Explanation:

Let us consider that the variables were inverted on purpose. That way, y is the horizontal axis and x is the vertical one.

First of all, solve the Mathematical Identitiy:

Then simplify the function:

From this point on, there are many ways to find the vertex. I prefer the one that doesn't use formulas. Every quadratic formula takes the shape of a parabola, and every parabola has a symmetry axis. That means points that have the same height have the same distance from the center. Therefore, let's calculate the roots:

Find the point that is between the roots:

Therefore, the axis is located at (3, -9).

graph{(x-3)^2-9 [-2, 8, -10, 10]}