Find the vertex for the following function \( y=2|x|-4 \) \( (4,0) \) \( (0,-4) \) \( (0,0) \) \( (-4,0) \)

The vertex of the function \( y = 2|x| - 4 \) is found by identifying the minimum point of the absolute value function. Since the absolute value function \( |x| \) has a vertex at \( (0,0) \), and this function is vertically stretched by a factor of 2 while being shifted down by 4 units, the vertex of the given function is at the point \( (0, -4) \). Now, let's think about the practical application of this concept! In real life, absolute value functions like this are often used to model situations where distance from a point is important, such as calculating travel costs based on how far you are from a specific location. In this context, the vertex indicates the minimum cost point, similar to how the vertex represents the minimum or maximum point in a parabolic graph! Don't forget, when working with absolute value equations, it's easy to get caught up in sign errors. A common mistake is not recognizing that the vertex of the function is the turning point where the slope changes. Always double-check whether you’ve understood how transformations affect the vertex's location!