describe the translations of the graph y=x^2 that results in the graph of y=x^2 - 7
The graph y = x^2 represents a parabola that opens upward and is centered at the origin.
When we add -7 to the function, we obtain the graph y = x^2 - 7. This translation causes the whole graph to shift downward by 7 units.
The vertex of the new graph is located at (0, -7) instead of the original (0, 0). The new parabola still opens upward, but it is lower on the y-axis compared to the original graph.
All other points on the graph are also shifted downward by 7 units. For example, if the original graph had a point (2, 4), the new graph would have the point (2, -3).
In summary, the translation of y = x^2 to y = x^2 - 7 results in a downward shift of the graph by 7 units, with its vertex now at (0, -7).