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f(x)=-(x+2)^(2)+16 Which of the following is an equivalent form of the function f in which the y-intercept of the graph of f appears as a constant or coefficient? Choose 1 answer: (A) f(x)=-(x-6)(x+2) (B) f(x)=-(x-2)(x+6) (c) f(x)=-x^(2)-4x+12 (D) f(x)=-x^(2)+4x+20

f(x)=−(x+2)2+16 f(x)=-(x+2)^{2}+16 \newlineWhich of the following is an equivalent form of the function f f in which the y y -intercept of the graph of f f appears as a constant or coefficient?\newlineChoose 11 answer:\newline(A) f(x)=−(x−6)(x+2) f(x)=-(x-6)(x+2) \newline(B) f(x)=−(x−2)(x+6) f(x)=-(x-2)(x+6) \newline(C) f(x)=−x2−4x+12 f(x)=-x^{2}-4 x+12 \newline(D) f(x)=−x2+4x+20 f(x)=-x^{2}+4 x+20

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Q. f(x)=−(x+2)2+16 f(x)=-(x+2)^{2}+16 \newlineWhich of the following is an equivalent form of the function f f in which the y y -intercept of the graph of f f appears as a constant or coefficient?\newlineChoose 11 answer:\newline(A) f(x)=−(x−6)(x+2) f(x)=-(x-6)(x+2) \newline(B) f(x)=−(x−2)(x+6) f(x)=-(x-2)(x+6) \newline(C) f(x)=−x2−4x+12 f(x)=-x^{2}-4 x+12 \newline(D) f(x)=−x2+4x+20 f(x)=-x^{2}+4 x+20
  1. Expand the given function: Expand the given function f(x)=−(x+2)2+16f(x) = -(x+2)^2 + 16 to find the y-intercept.\newlineTo expand, apply the square to the binomial (x+2)2(x+2)^2 and then multiply by −1-1.\newline(x+2)2=x2+4x+4(x+2)^2 = x^2 + 4x + 4\newlineNow, multiply by −1-1 to get:\newline−(x2+4x+4)=−x2−4x−4-(x^2 + 4x + 4) = -x^2 - 4x - 4\newlineFinally, add 1616 to get the expanded form:\newlinef(x)=−x2−4x−4+16f(x) = -x^2 - 4x - 4 + 16\newlineSimplify the constant terms:\newlinef(x)=−x2−4x+12f(x) = -x^2 - 4x + 12
  2. Identify the y-intercept: Identify the y-intercept in the expanded form.\newlineThe y-intercept of a function is the value of the function when x=0x = 0.\newlineIn the expanded form f(x)=−x2−4x+12f(x) = -x^2 - 4x + 12, when x=0x = 0, f(0)=12f(0) = 12.\newlineThis means the y-intercept is 1212.
  3. Compare with given choices: Compare the expanded form with the given choices to find the equivalent form that shows the y-intercept as a constant or coefficient.\newlineThe expanded form is f(x)=−x2−4x+12f(x) = -x^2 - 4x + 12.\newlineNow, let's check the choices:\newline(A) f(x)=−(x−6)(x+2)f(x) = -(x-6)(x+2) does not match the expanded form.\newline(B) f(x)=−(x−2)(x+6)f(x) = -(x-2)(x+6) does not match the expanded form.\newline(C) f(x)=−x2−4x+12f(x) = -x^2 - 4x + 12 matches the expanded form and shows the y-intercept as 1212.\newline(D) f(x)=−x2+4x+20f(x) = -x^2 + 4x + 20 does not match the expanded form.

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