Question
Which key feature helps to clearly illustrate that this graph has been moved down 3 units from the
parent function y = x
2?
(1 point)
the y-intercept
the graph’s rate of change
the direction the graph opens
the symmetry of the graph
parent function y = x
2?
(1 point)
the y-intercept
the graph’s rate of change
the direction the graph opens
the symmetry of the graph
Answers
GPT-4o mini
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**.
When a graph of a function is translated vertically, such as moving down 3 units in this case, the y-intercept will also change accordingly. For the parent function \( y = x^2 \), the y-intercept is 0 (when \( x = 0 \), \( y = 0^2 = 0 \)). After moving down 3 units, the new function would be \( y = x^2 - 3 \), and its y-intercept would be -3. Thus, examining the y-intercept directly illustrates the vertical shift of the graph.
When a graph of a function is translated vertically, such as moving down 3 units in this case, the y-intercept will also change accordingly. For the parent function \( y = x^2 \), the y-intercept is 0 (when \( x = 0 \), \( y = 0^2 = 0 \)). After moving down 3 units, the new function would be \( y = x^2 - 3 \), and its y-intercept would be -3. Thus, examining the y-intercept directly illustrates the vertical shift of the graph.