2
advanced-math

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

A

y=(x+1)(x−5)y = (x + 1)(x - 5)

B

y=(x−1)(x+5)y = (x - 1)(x + 5)

C

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

D

y=(x−1)(x−5)y = (x - 1)(x - 5)

Correct Answer: A

Choice A is the correct answer. If x=−1x = -1 is a root, then (x+1)(x + 1) is a factor. If x=5x = 5 is a root, then (x−5)(x - 5) is a factor. The equation is the product of these factors: y=a(x+1)(x−5)y = a(x + 1)(x - 5).

Choice B is incorrect because intercepts would be 1,−51, -5. Choice C is incorrect because intercepts would be −1,−5-1, -5. Choice D is incorrect because intercepts would be 1,51, 5.

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Set 9: Quadratic Equations and Functions 9