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Rewrite the function by completing the square. {:[f(x)=x^(2)+14 x+64],[f(x)=(x+◻)^(2)+◻]:}

Rewrite the function by completing the square.\newlinef(x)=x2+14x+64 f(x) = x^2 + 14x + 64 \newlinef(x)=(x+□)2+□ f(x) = (x+\square)^2 + \square

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Q. Rewrite the function by completing the square.\newlinef(x)=x2+14x+64 f(x) = x^2 + 14x + 64 \newlinef(x)=(x+□)2+□ f(x) = (x+\square)^2 + \square
  1. Identify coefficient of x: To complete the square, we need to form a perfect square trinomial from the quadratic and linear terms of the function f(x)=x2+14x+64f(x) = x^2 + 14x + 64.\newlineFirst, we identify the coefficient of xx, which is 1414, and then divide it by 22 and square the result to find the number that we need to add and subtract to complete the square.\newline(142)2=72=49\left(\frac{14}{2}\right)^2 = 7^2 = 49.
  2. Add and subtract to complete the square: We add and subtract 4949 inside the function to complete the square.\newlinef(x)=x2+14x+49−49+64.f(x) = x^2 + 14x + 49 - 49 + 64.
  3. Rewrite the function: Now we can rewrite the function by factoring the perfect square trinomial and combining the constants. \newlinef(x)=(x+7)2−49+64f(x) = (x + 7)^2 - 49 + 64.
  4. Combine the constants: Combine the constants −49-49 and +64+64 to simplify the function.f(x)=(x+7)2+15.f(x) = (x + 7)^2 + 15.

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