Set 8: Quadratic Equations (Intermediate)

Explanation

Answer: A

Which equation represents $y = x^2$ shifted down 5 units?

$y = x^2 - 5$

✓ Correct

$y = x^2 + 5$

$y = (x - 5)^2$

$y = (x + 5)^2$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Vertical shifts are represented by the constant $k$ added outside the squared term ( $y = x^2 + k$ ). 1. To shift down 5 units, we subtract 5. 2. Result: $y = x^2 - 5$ . Choice B is incorrect because this shifts up. Choice C is incorrect because this shifts right. Choice D is incorrect because this shifts left.

Key Steps:

•

The correct answer is $y = x^2 - 5$

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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