Comparing Vertices: When is x² Equal to 2x² at the Same Point?

The given functions are $y = x^2$ and $y = 2x^2$. Both functions are written in the form $y = ax^2$, where the vertex for such parabolas is determined by setting $x = 0$.

Let's analyze each function step-by-step:

• Function $y = x^2$:
  This function represents a parabola that opens upwards with its vertex located at $(0, 0)$.
• Function $y = 2x^2$:
  Similarly, this function is also a parabola that opens upwards. The coefficient $2$ affects the "narrowness" or "width" of the parabola but does not shift the vertex, so the vertex remains at $(0, 0)$.

Both functions $y = x^2$ and $y = 2x^2$ share the same vertex at the point $(0, 0)$. Therefore, the statement that the vertex of the function $y=x^2$ is the same vertex of the function $y=2x^2$ is True.

Thus, the correct answer to the problem is True.