Set 17: Quadratic Equations (Advanced)

Explanation

Answer: A

A graph shows x-intercepts at -1 and 5. Which equation could represent this graph?

$y = (x + 1)(x - 5)$

✓ Correct

$y = (x - 1)(x + 5)$

$y = (x + 1)(x + 5)$

$y = (x - 1)(x - 5)$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. If $x = -1$ is a root, then $(x + 1)$ is a factor. If $x = 5$ is a root, then $(x - 5)$ is a factor. The equation is the product of these factors: $y = a(x + 1)(x - 5)$ . Choice B is incorrect because intercepts would be $1, -5$ . Choice C is incorrect because intercepts would be $-1, -5$ . Choice D is incorrect because intercepts would be $1, 5$ .

Key Steps:

•

The correct answer is $y = (x + 1)(x - 5)$

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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