Set 15: Quadratic Equations

Explanation

Answer: A

Convert $y = 2(x - 1)^2 + 3$ to standard form.

$y = 2x^2 - 4x + 5$

✓ Correct

$y = 2x^2 - 2x + 5$

$y = 2x^2 - 4x + 4$

$y = 2x^2 + 5$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Follow the order of operations (PEMDAS): Exponents first, then Multiplication, then Addition. 1. Expand: $(x - 1)^2 = x^2 - 2 x + 1$ . 2. Distribute: $2(x^2 - 2 x + 1) = 2 x^2 - 4 x + 2$ . 3. Add: $(2 x^2 - 4 x + 2) + 3 = 2 x^2 - 4 x + 5$ . Choice B is incorrect because it forgets to distribute the 2 to the middle term ( $-2 x$ ). Choice C is incorrect because $2 +3=5$ , not 4. Choice D is incorrect because it ignores the middle term entirely.

Key Steps:

•

The correct answer is $y = 2x^2 - 4x + 5$

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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Set 15: Quadratic Equations

Detailed Explanation

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