Question
Which key feature helps to clearly illustrate that this graph has been moved down 3 units from the parent function y=x2
?
(1 point)
Responses
the symmetry of the graph
the symmetry of the graph
the graph’s rate of change
the graph’s rate of change
the y-intercept
the y- intercept
the direction the graph opens
?
(1 point)
Responses
the symmetry of the graph
the symmetry of the graph
the graph’s rate of change
the graph’s rate of change
the y-intercept
the y- intercept
the direction the graph opens
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 you move the graph of \(y = x^2\) down by 3 units, the new equation becomes \(y = x^2 - 3\). The y-intercept of the graph is where the graph crosses the y-axis, and moving down 3 units changes the y-intercept from 0 (at \(y = x^2\)) to -3 (at \(y = x^2 - 3\)).
When you move the graph of \(y = x^2\) down by 3 units, the new equation becomes \(y = x^2 - 3\). The y-intercept of the graph is where the graph crosses the y-axis, and moving down 3 units changes the y-intercept from 0 (at \(y = x^2\)) to -3 (at \(y = x^2 - 3\)).