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Write the quadratic equation that contains the following transformations. Remember, the quadratic parent...

Write the quadratic equation that contains the following transformations.
Remember, the quadratic parent function is y = x².
• Vertical Compression by a factor of 1/2
• Reflection over the x-axis
• Translation 6 units up
• Translation 3 units right

Answer

y = −(1/2)(x − 3)² + 6

The coefficient −1/2 compresses the parabola vertically by a factor of 1/2 and reflects it over the x-axis. Replacing x with x − 3 shifts it 3 units right, and adding 6 shifts it 6 units up.

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