Question
graph shows a red line curves and ends at (0,0) and a blue dotted line curves and ends at (4,0)
which of the following correctly determines how many k
units the parent function y=x2
(shown as a solid line) was shifted horizontally.
(1 point)
Responses
The parent function was shifted 5 units to the left.
The parent function was shifted 5 units to the left.
The parent function was shifted 4 units to the left.
The parent function was shifted 4 units to the left.
The parent function was shifted 4 units to the right.
The parent function was shifted 4 units to the right.
The parent function was shifted 5 units to the right.
which of the following correctly determines how many k
units the parent function y=x2
(shown as a solid line) was shifted horizontally.
(1 point)
Responses
The parent function was shifted 5 units to the left.
The parent function was shifted 5 units to the left.
The parent function was shifted 4 units to the left.
The parent function was shifted 4 units to the left.
The parent function was shifted 4 units to the right.
The parent function was shifted 4 units to the right.
The parent function was shifted 5 units to the right.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine how many units the parent function \( y = x^2 \) has been shifted horizontally based on the information given:
- The red line curves and ends at (0,0).
- The blue dotted line curves and ends at (4,0).
The parent function \( y = x^2 \) has its vertex at (0,0). If we look at the blue dotted line, which ends at (4,0), it means that the vertex of the shifted function \( y = (x - h)^2 \) is now at (4,0).
For a quadratic function of the form \( y = (x - h)^2 \), a positive \( h \) indicates a shift to the right, and a negative \( h \) indicates a shift to the left.
Since the vertex has moved from (0,0) to (4,0), we see that it has shifted **4 units to the right**.
Thus, the correct response is:
**The parent function was shifted 4 units to the right.**
- The red line curves and ends at (0,0).
- The blue dotted line curves and ends at (4,0).
The parent function \( y = x^2 \) has its vertex at (0,0). If we look at the blue dotted line, which ends at (4,0), it means that the vertex of the shifted function \( y = (x - h)^2 \) is now at (4,0).
For a quadratic function of the form \( y = (x - h)^2 \), a positive \( h \) indicates a shift to the right, and a negative \( h \) indicates a shift to the left.
Since the vertex has moved from (0,0) to (4,0), we see that it has shifted **4 units to the right**.
Thus, the correct response is:
**The parent function was shifted 4 units to the right.**
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