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The parabola $y=x^2$ is scaled vertically by a factor of $\frac{1}{10}$ . What is the equation of the new parabola?

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Write a quadratic function in vertex form

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Q. The parabola

y=x^2

is scaled vertically by a factor of

\frac{1}{10}

. What is the equation of the new parabola?

Multiply output by $\frac{1}{10}$ : To scale the parabola $y = x^2$ vertically by a factor of $\frac{1}{10}$ , we multiply the output (y-value) by $\frac{1}{10}$ .
Update equation: The original equation is $y = x^2$ . After scaling, the new equation becomes $y = \frac{1}{10}x^2$ .
Check for correct scaling: Check the new equation to ensure that the scaling factor has been applied correctly. The original parabola $y = x^2$ , when scaled by $\frac{1}{10}$ , should result in the $y$ -values being $\frac{1}{10}$ th of the original $y$ -values. For example, if $x = 2$ , the original $y$ -value is $2^2 = 4$ . The new $y$ -value should be $\frac{1}{10}$ of $\frac{1}{10}$ $0$ , which is $\frac{1}{10}$ $1$ . Substituting $x = 2$ into the new equation gives $\frac{1}{10}$ $3$ , which is correct.

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