Which of these functions has zeros of x=−16 and x=16?
A
f(x)=x^2−16
B
f(x)=x^2−256
C
f(x)=x^2−32x+256
D
f(x)=x^2+32x+256
Question
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Answer:b) f(x) = x² – 256Step-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:brainly.com/question/18033939brainly.com/question/27638369