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The parabola
y=x^(2) is reflected across the
x-axis and then scaled vertically by a factor of 5 .
What is the equation of the new parabola?

y=

The parabola $y=x^{2}$ is reflected across the $x$ -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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Transformations of functions

Full solution

Q. The parabola

y=x^{2}

is reflected across the

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 need to multiply the $y$ -values by $-1$ . This reflection changes the sign of the $y$ -values, turning the parabola upside down.
New equation after reflection: The equation of the parabola after reflection across the x-axis is $y = -x^2$ .
Scaling vertically by a factor: Scaling the parabola vertically by a factor of $5$ means we need to multiply the $y$ -values by $5$ . This scaling stretches or compresses the parabola in the vertical direction.
New equation after vertical scaling: The equation of the parabola after scaling vertically by a factor of $5$ is $y = 5(-x^2)$ . We can simplify this by distributing the $5$ into the parentheses.
Final equation: The final equation of the new parabola is $y = -5x^2$ .

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