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The parabola $\newline$ $y=x^{2}$ is reflected across the $\newline$ $x$ -axis and then scaled vertically by a factor of $5$ . $\newline$ What is the equation of the new parabola? $\newline$ $y=\square$

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Find the vertex of the transformed function

Full solution

Q. The parabola

\newline

y=x^{2}

is reflected across the

\newline

x

-axis and then scaled vertically by a factor of

5

.

\newline

What is the equation of the new parabola?

\newline

y=\square

Reflecting the parabola: Reflecting the parabola $y = x^2$ across the $x$ -axis means we change the sign of the $y$ -values. This reflection is represented by multiplying the original function by $-1$ .
Changing sign of y-values: The equation of the parabola after reflection across the x-axis is $y = -x^2$ .
Scaling vertically by factor: Scaling the reflected parabola vertically by a factor of $5$ means we multiply the $y$ -values by $5$ . This scaling is represented by multiplying the reflected function by $5$ .
Multiplying $y$ -values by $5$ : The equation of the new parabola after scaling is $y = 5(-x^2)$ .
Simplifying the equation: Simplify the equation by distributing the $5$ into the parentheses. $y = -5x^2$

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