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f(x)=(x+2)^(2)-64 At what values of x does the graph of the function intersect the x-axis? Choose 1 answer: (A) x=6,x=-10 (B) x=6,x=10 (c) x=-6,x=-10 (D) f(x) does not intersect the x-axis.

f(x)=(x+2)2−64 f(x)=(x+2)^{2}-64 \newlineAt what values of x x does the graph of the function intersect the x x -axis?\newlineChoose 11 answer:\newline(A) x=6,x=−10 x=6, x=-10 \newline(B) x=6,x=10 x=6, x=10 \newline(C) x=−6,x=−10 x=-6, x=-10 \newline(D) f(x) f(x) does not intersect the x x -axis.

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Q. f(x)=(x+2)2−64 f(x)=(x+2)^{2}-64 \newlineAt what values of x x does the graph of the function intersect the x x -axis?\newlineChoose 11 answer:\newline(A) x=6,x=−10 x=6, x=-10 \newline(B) x=6,x=10 x=6, x=10 \newline(C) x=−6,x=−10 x=-6, x=-10 \newline(D) f(x) f(x) does not intersect the x x -axis.
  1. Problem Understanding: Understand the problem.\newlineWe need to find the values of xx for which f(x)=0f(x) = 0, because the graph of the function intersects the xx-axis where the function value is zero.
  2. Equation Setup: Set the function equal to zero and solve for x.\newlinef(x) = (x+22)^22 - 6464 = 00
  3. Quadratic Equation Solution: Solve the quadratic equation.\newline(x+2)2=64(x+2)^2 = 64\newlineTake the square root of both sides.\newlinex+2=±64x+2 = \pm\sqrt{64}\newlinex+2=±8x+2 = \pm8
  4. Solving for x: Solve for x.\newlinex=−2+8x = -2 + 8 or x=−2−8x = -2 - 8\newlinex=6x = 6 or x=−10x = -10
  5. Solution Verification: Check the solutions.\newlinePlug x=6x = 6 and x=−10x = -10 back into the function to ensure they result in f(x)=0f(x) = 0.\newlinef(6)=(6+2)2−64=64−64=0f(6) = (6+2)^2 - 64 = 64 - 64 = 0\newlinef(−10)=(−10+2)2−64=144−64=80f(-10) = (-10+2)^2 - 64 = 144 - 64 = 80\newlineThere is a math error in the calculation for f(−10)f(-10). The correct calculation should be:\newlinef(−10)=(−10+2)2−64=(−8)2−64=64−64=0f(-10) = (-10+2)^2 - 64 = (-8)^2 - 64 = 64 - 64 = 0

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