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The parabola \( y=x^{2} \) is scaled vertically by a factor of 7 . What is the equation of the new parabola? \( y=\square \)

Ask by George Potter. in the United States
Feb 22,2025

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The new equation is \( y = 7x^{2} \).

Solución

A vertical scaling by a factor of 7 multiplies the output (y-coordinate) of the original function by 7. Since the original function is y = x², the new function becomes: y = 7x².

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When you scale a function vertically, you multiply the entire function by the scaling factor. For the parabola \( y = x^2 \), scaling it vertically by a factor of 7 means taking each output value of \( y \) and multiplying it by 7. Thus, the equation of the new parabola becomes \( y = 7x^2 \). So, the equation of the new parabola is \( y = 7x^2 \).

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