Question
A parabola that opens upward and seven labeled points on the parabola are plotted on a coordinate plane. The parabola has bidirectional arrows and is labeled f left parenthesis x right parenthesis equals x squared baseline minus 3.
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 y-intercept
the y- intercept
the direction the graph opens
the direction the graph opens
the graph’s rate of change
the graph’s rate of change
the symmetry of the graph
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 y-intercept
the y- intercept
the direction the graph opens
the direction the graph opens
the graph’s rate of change
the graph’s rate of change
the symmetry of the graph
Answers
GPT-4o mini
The key feature that helps to clearly illustrate that this graph has been moved down 3 units from the parent function \( y = x^2 \) is **the y-intercept**.
The function \( f(x) = x^2 - 3 \) has a y-intercept at \( (0, -3) \), while the parent function \( y = x^2 \) has a y-intercept at \( (0, 0) \). This shift in the y-intercept is a clear indicator of the graph being moved down 3 units.
The function \( f(x) = x^2 - 3 \) has a y-intercept at \( (0, -3) \), while the parent function \( y = x^2 \) has a y-intercept at \( (0, 0) \). This shift in the y-intercept is a clear indicator of the graph being moved down 3 units.