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f(x)=(x-2)^(2)-9 At what values of x does the graph of the function intersect the x-axis? Choose 1 answer: (A) x=-5,x=-1 (B) x=5,x=1 (c) x=-5,x=1 (D) x=5,x=-1

f(x)=(x−2)2−9 f(x)=(x-2)^{2}-9 \newlineAt what values of x x does the graph of the function intersect the x x -axis?\newlineChoose 11 answer:\newline(A) x=−5,x=−1 x=-5, x=-1 \newline(B) x=5,x=1 x=5, x=1 \newline(C) x=−5,x=1 x=-5, x=1 \newline(D) x=5,x=−1 x=5, x=-1

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Q. f(x)=(x−2)2−9 f(x)=(x-2)^{2}-9 \newlineAt what values of x x does the graph of the function intersect the x x -axis?\newlineChoose 11 answer:\newline(A) x=−5,x=−1 x=-5, x=-1 \newline(B) x=5,x=1 x=5, x=1 \newline(C) x=−5,x=1 x=-5, x=1 \newline(D) x=5,x=−1 x=5, x=-1
  1. Set equation to zero: The question prompt is: ＂At what values of xx does the graph of the function f(x)=(x−2)2−9f(x) = (x-2)^{2} - 9 intersect the x-axis?＂\newlineTo find the x-intercepts of the function, we need to set f(x)f(x) to zero and solve for xx.\newlineSo, we set the equation (x−2)2−9=0(x-2)^{2} - 9 = 0.
  2. Solve the equation: Now we solve the equation (x−2)2−9=0(x-2)^{2} - 9 = 0.\newlineWe can rewrite this as (x−2)2=9(x-2)^{2} = 9.\newlineTaking the square root of both sides, we get x−2=±3x - 2 = \pm3.
  3. Positive root: We solve for x by adding 22 to both sides of the equations.\newlineFor the positive root: x−2=3x - 2 = 3 leads to x=3+2x = 3 + 2, which gives us x=5x = 5.\newlineFor the negative root: x−2=−3x - 2 = -3 leads to x=−3+2x = -3 + 2, which gives us x=−1x = -1.
  4. Negative root: We have found two values of xx where the function intersects the xx-axis: x=5x = 5 and x=−1x = -1. These are the xx-intercepts of the function.

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