To determine how many units the parent function \( y = x^2 \) was translated, we need to compare the vertex or the starting point of the solid line (the transformed parabola) to the vertex of the parent function.
Assuming the parent function has its vertex at the origin (0,0), an x-value of the transformed function indicates how far it has been translated horizontally.
From the options provided:
- If the vertex of the solid line parabola is at \( x = 5 \) (for instance), it would mean the parent function was translated 5 units to the right, since \( 0 + 5 = 5 \).
- If the vertex of the solid line parabola is at \( x = -6 \), it would then mean the parent function was translated 6 units to the left, since \( 0 - 6 = -6 \).
However, without an actual image to reference, we cannot determine its exact position. Here's how you can confirm the translation based on the vertex of the solid line:
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If the solid line's vertex is at \( x = 5 \), the answer is:
- "The parent function was translated 5 units to the right."
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If the solid line's vertex is at \( x = 6 \), the answer is:
- "The parent function was translated 6 units to the right."
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If the solid line's vertex is at \( x = -5 \), the answer is:
- "The parent function was translated 5 units to the left."
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If the solid line's vertex is at \( x = -6 \), the answer is:
- "The parent function was translated 6 units to the left."
Review the image carefully to find the x-coordinate of the vertex of the solid line, then select the appropriate option based on that position.
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