To provide the parent function and the transformed function, I need to know the nature of the transformation applied to the parabolic graph. However, since the graph hasn't been visually presented here, I can provide you with general information on how to write these functions based on common transformations.
Parent Function: The parent function of a parabola is given by: \[ y = x^2 \]
Transformed Function: Transformations can include shifts (translations), vertical or horizontal stretches/compressions, and reflections. Here are a few examples of each type of transformation:
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Vertical Shift: If the parabola shifts up by \(k\), then the function becomes: \[ y = x^2 + k \] If it shifts down by \(k\), then use: \[ y = x^2 - k \]
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Horizontal Shift: If the parabola shifts right by \(h\), then the function becomes: \[ y = (x - h)^2 \] If it shifts left by \(h\), then use: \[ y = (x + h)^2 \]
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Vertical Stretch/Compression: If the parabola is vertically stretched by a factor of \(a\), then the function becomes: \[ y = a(x^2) \] If compressed, \(0 < a < 1\), then it's still the same form.
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Reflection: If there's a reflection over the x-axis, the function becomes: \[ y = -x^2 \]
To combine these transformations, you would create a general transformation form: \[ y = a(x - h)^2 + k \] Where \(a\) determines vertical stretching/compression and reflection, \((h, k)\) shifts the graph horizontally and vertically.
To write the specific transformed function, I would need details about the transformation, such as shifts or flips. If you can describe the transformation or characteristics of the graph (movement, direction, etc.), I could provide a specific transformed function.