Answer:
b) f(x) = x² - 256
Step-by-step explanation:
Since we have been given the zeros of a function, -16 and 16. We are asked to find which function truly has those zeros.
To find this, we can substitute the zeros for x in the functions to find the one that is true/correct.
A) f(x) = x² - 16
⇒ 0 = 16² - 16 and ⇒ 0 = (-16)² - 16
⇒ 0 = 256 - 16 and ⇒ 0 = 256 - 16
⇒ 0 = 240 ✘ and ⇒ 0 = 240 ✘
B) f(x) = x² - 256
⇒ 0 = 16² - 256 and ⇒ 0 = (-16)² - 256
⇒ 0 = 256 - 256 and ⇒ 0 = 256 - 256
⇒ 0 = 0 ✔ and ⇒ 0 = 0 ✔
C) f(x) = x² - 32x + 256
⇒ 0 = 16² - 32(16) + 256 and ⇒ 0 = (-16)² - 32(-16) + 256
⇒ 0 = 256 - 512 + 256 and ⇒ 0 = 256 + 512 + 256
⇒ 0 = 512 - 512 and ⇒ 0 = 512 + 512
⇒ 0 = 0 ✔ and ⇒ 0 = 1,024 ✘
D) f(x) = x² + 32x + 256
⇒ 0 = 16² + 32(16) + 256 and ⇒ 0 = (-16)² + 32(-16) + 256
⇒ 0 = 256 + 512 + 256 and ⇒ 0 = 256 - 512 + 256
⇒ 0 = 512 + 512 and ⇒ 0 = 512 - 512
⇒ 0 = 1,024 ✘ and ⇒ 0 = 0 ✔
Therefore, Function B has the zeros of x = -16 and x = 16.
Learn more about finding the zeros of a function here:
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