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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. Show calculator

f(x)=(x+22)^{22}−64-64 At what values of x does the graph of the function intersect the x-axis? Choose 11 answer:\newline(A) \newlinex=66,x=−10-10\newline(B) \newlinex=66,x=1010\newline(C) \newlinex=−6-6,x=−10-10\newlineD \newlinef(x) does not intersect the \newlinex-axis.

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Q. f(x)=(x+22)^{22}−64-64 At what values of x does the graph of the function intersect the x-axis? Choose 11 answer:\newline(A) \newlinex=66,x=−10-10\newline(B) \newlinex=66,x=1010\newline(C) \newlinex=−6-6,x=−10-10\newlineD \newlinef(x) does not intersect the \newlinex-axis.
  1. Set f(x)f(x) to 00: First, set f(x)f(x) to 00 because the graph intersects the xx-axis where f(x)=0f(x) = 0. 0=(x+2)2−640 = (x + 2)^2 - 64
  2. Add 6464 to isolate: Add 6464 to both sides to isolate the squared term. 64=(x+2)264 = (x + 2)^2
  3. Take square root: Take the square root of both sides to solve for x+2x + 2. 64=x+2\sqrt{64} = x + 2 8=x+28 = x + 2 or −8=x+2-8 = x + 2
  4. Solve for x: Solve for xx in both equations. x=8−2=6x = 8 - 2 = 6 x=−8−2=−10x = -8 - 2 = -10
  5. Check solutions: Check the solutions by substituting back into the original equation. For x=6x = 6: f(6)=(6+2)2−64=64−64=0f(6) = (6 + 2)^2 - 64 = 64 - 64 = 0 For x=−10x = -10: f(−10)=(−10+2)2−64=64−64=0f(-10) = (-10 + 2)^2 - 64 = 64 - 64 = 0 Both solutions are correct.

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