The transition from the graph of y = 2x² to the graph of y = 2x² + 5 can best be described as a vertical shift upwards by 5 units.
To understand this, let’s break down the equation:
- The original graph, y = 2x², is a standard parabola that opens upwards with its vertex located at the origin (0,0).
- When we add 5 to the original equation to get y = 2x² + 5, each point on the graph of y = 2x² is increased by 5 on the y-axis.
This means that the entire shape of the graph remains the same—its width and direction do not change—but its position on the coordinate plane does change.
In summary, you can think of it as lifting the entire parabola 5 units higher, which effectively translates all points of the original graph upwards without altering their horizontal locations.