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The parabola
y=x^(2) is scaled vertically by a factor of
(2)/(3).
What is the equation of the new parabola?

y=

The parabola $y=x^{2}$ is scaled vertically by a factor of $\frac{2}{3}$ . $\newline$ What is the equation of the new parabola? $\newline$ $y=$

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Transformations of functions

Full solution

Q. The parabola

y=x^{2}

is scaled vertically by a factor of

\frac{2}{3}

.

\newline

What is the equation of the new parabola?

\newline

y=

Scaling the Parabola: To scale the parabola $y = x^2$ vertically by a factor of $\frac{2}{3}$ , we multiply the output ( $y$ -value) of the function by $\frac{2}{3}$ . This means that every $y$ -value of the original parabola will be multiplied by $\frac{2}{3}$ to get the new $y$ -value of the scaled parabola.
Multiplying the Y-Values: The equation of the original parabola is $y = x^2$ . To scale it vertically by a factor of $\frac{2}{3}$ , we apply the scaling factor to the y-value. The new equation becomes $y = \left(\frac{2}{3}\right)x^2$ .

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