Which key feature helps to clearly illustrate that this graph has been moved down 3 units from the parent function y = x^2

Question

Graph is an upward u shape with points (0,3),(-1,-2),(1,-2),(-2,1),(2,1),(-3,6),(3,6),
f(x)= x^2-3
The direction the graph opens
The y -intercept
The graphs rate of change
The symmetry of the graph

Answer 1

The key feature that helps to clearly illustrate that the graph has been moved down 3 units from the parent function \( y = x^2 \) is the y-intercept.

For the parent function \( y = x^2 \), the y-intercept is at \( (0, 0) \). For the transformed function \( f(x) = x^2 - 3 \), the y-intercept is at \( (0, -3) \). The downward shift of 3 units is directly reflected in this change of the y-intercept from 0 to -3.

While the direction the graph opens, the rate of change, and the symmetry of the graph are also important characteristics, they do not directly indicate the vertical shift of the graph. Therefore, the y-intercept is the most relevant feature to illustrate the downward movement.