To determine how many units the parent function \( y = x^2 \) was translated, you typically look at the vertex of the translated parabola compared to the vertex of the parent function.
The parent function \( y = x^2 \) has its vertex at the origin (0, 0). If the new parabola (shown as a solid line) has its vertex at a point (h, k), then we determine the translation along the x-axis by calculating \( h \).
- If \( h \) is positive, the graph has moved \( h \) units to the right.
- If \( h \) is negative, the graph has moved \( |h| \) units to the left.
Given that the two parabolas are drawn on a coordinate plane from x = -9 to x = 4 and you didn't mention the specific coordinates of the vertex for the translated parabola, we cannot provide an exact numerical answer without further information.
Please refer to the vertex of the translated parabola to calculate the translation accurately. If for instance the vertex of the translated parabola is at (5, y), then it has been translated 5 units to the right. If the vertex of the translated parabola is at (-6, y), then it has been translated 6 units to the left.
Based on your question, if the translated parabola's vertex is at \( (6, y) \), the correct response would be "The parent function was translated 6 units to the right." Conversely, if it's at \( (-5, y) \), then it would be "The parent function was translated 5 units to the left."
Please confirm the coordinates for precise identification.
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