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Given the function f(x)=-4x^(2)+5, then what is f(x-2) as a simplified polynomial? Answer:

Given the function f(x)=−4x2+5 f(x)=-4 x^{2}+5 , then what is f(x−2) f(x-2) as a simplified polynomial?\newlineAnswer:

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Q. Given the function f(x)=−4x2+5 f(x)=-4 x^{2}+5 , then what is f(x−2) f(x-2) as a simplified polynomial?\newlineAnswer:
  1. Substitute x−2x-2: Substitute (x−2)(x-2) for xx in the function f(x)=−4x2+5f(x)=-4x^2+5.\newlinef(x−2)=−4(x−2)2+5f(x-2) = -4(x-2)^2 + 5
  2. Expand square: Expand the square (x−2)2(x-2)^2.(x−2)2=x2−4x+4(x-2)^2 = x^2 - 4x + 4
  3. Substitute expanded square: Substitute the expanded square into the function.\newlinef(x−2)=−4(x2−4x+4)+5f(x-2) = -4(x^2 - 4x + 4) + 5
  4. Distribute −4-4: Distribute the −4-4 across the terms in the parentheses.\newlinef(x−2)=−4x2+16x−16+5f(x-2) = -4x^2 + 16x - 16 + 5
  5. Combine constant terms: Combine the constant terms −16-16 and 55.f(x−2)=−4x2+16x−11f(x-2) = -4x^2 + 16x - 11

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