To interpret the key features of the graph of an upward open parabola that passes through certain plotted points, we should focus on the nature of how the parabola's shape has changed compared to the parent function \(y = x^2\).
A vertical stretch occurs when the parabola becomes narrower than the standard \(y = x^2\) shape. This happens when the y-coordinates of the points on the curve are further away from the x-axis compared to \(y = x^2\). The x-coordinates of the points would typically not directly affect a vertical stretch from \(y = x^2\), indicating that the transformation is more about the scale in the y-direction rather than the x-direction.
Among the response options you've provided, the correct one that accurately describes this transformation would be:
This is a vertical stretch of the parent function \(y=x^2\) due to the changes in the y-coordinates of each point.
This response clearly indicates that the vertical stretch is influenced by how the y-coordinates of the plotted points differ from those of the parent function, which reveals the relative scaling effect that is characteristic of vertical transformations.