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The parabola $y = (x - 3)^2 - 2$ is reflected about the $y$-axis - HSC - SSCE Mathematics Advanced - Question 4 - 2024 - Paper 1

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The-parabola-$y-=-(x---3)^2---2$-is-reflected-about-the-$y$-axis-HSC-SSCE Mathematics Advanced-Question 4-2024-Paper 1.png

The parabola $y = (x - 3)^2 - 2$ is reflected about the $y$-axis. This is then reflected about the $x$-axis. What is the equation of the resulting parabola? A. $y ... show full transcript

Worked Solution & Example Answer:The parabola $y = (x - 3)^2 - 2$ is reflected about the $y$-axis - HSC - SSCE Mathematics Advanced - Question 4 - 2024 - Paper 1

Step 1

Reflecting about the y-axis

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Answer

To reflect the parabola y=(x−3)2−2y = (x - 3)^2 - 2 about the yy-axis, we replace xx with −x-x. This gives us:

y=(−x−3)2−2y = (-x - 3)^2 - 2

Expanding this, we have:

y=(x+3)2−2y = (x + 3)^2 - 2

Step 2

Reflecting about the x-axis

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Answer

Next, we reflect the resulting parabola y=(x+3)2−2y = (x + 3)^2 - 2 about the xx-axis by negating yy:

−y=(x+3)2−2-y = (x + 3)^2 - 2

Rearranging this, we get:

y=−(x+3)2+2y = - (x + 3)^2 + 2

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