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Given the function f(x)=6x-x^(2), then what is f(x+2) as a simplified polynomial? Answer:

Given the function f(x)=6x−x2 f(x)=6 x-x^{2} , then what is f(x+2) f(x+2) as a simplified polynomial?\newlineAnswer:

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Q. Given the function f(x)=6x−x2 f(x)=6 x-x^{2} , then what is f(x+2) f(x+2) as a simplified polynomial?\newlineAnswer:
  1. Plug x+2x+2 into function: First we need to plug x+2x+2 into the function f(x)f(x).\newlinef(x+2)=6(x+2)−(x+2)2f(x+2) = 6(x+2) - (x+2)^2
  2. Distribute 66 into (x+2)(x+2): Now let's distribute the 66 into (x+2)(x+2).f(x+2)=6x+12−(x+2)2f(x+2) = 6x + 12 - (x+2)^2
  3. Expand (x+2)2(x+2)^2: Next, we need to expand (x+2)2.(x+2)^2.\newlinef(x+2)=6x+12−(x2+4x+4)f(x+2) = 6x + 12 - (x^2 + 4x + 4)
  4. Distribute negative sign: Then we distribute the negative sign into the expanded quadratic. f(x+2)=6x+12−x2−4x−4f(x+2) = 6x + 12 - x^2 - 4x - 4
  5. Combine like terms: Now we combine like terms. f(x+2)=−x2+2x+8f(x+2) = -x^2 + 2x + 8

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