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f(x)=(x+2)^(2)-16 At what values of x does the graph of the function intersect the x-axis? Choose 1 answer: (A) x=2,x=-6 (B) x=2,x=6 (c) x=-2,x=-6 (D) f(x) does not intersect the x-axis.

f(x)=(x+2)2−16 f(x)=(x+2)^{2}-16 \newlineAt what values of x x does the graph of the function intersect the x x -axis?\newlineChoose 11 answer:\newline(A) x=2,x=−6 x=2, x=-6 \newline(B) x=2,x=6 x=2, x=6 \newline(C) x=−2,x=−6 x=-2, x=-6 \newline(D) f(x) f(x) does not intersect the x x -axis.

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Q. f(x)=(x+2)2−16 f(x)=(x+2)^{2}-16 \newlineAt what values of x x does the graph of the function intersect the x x -axis?\newlineChoose 11 answer:\newline(A) x=2,x=−6 x=2, x=-6 \newline(B) x=2,x=6 x=2, x=6 \newline(C) x=−2,x=−6 x=-2, x=-6 \newline(D) f(x) f(x) does not intersect the x x -axis.
  1. Problem: The question_prompt: At what values of xx does the graph of the function f(x)=(x+2)2−16f(x) = (x+2)^2 - 16 intersect the xx-axis?
  2. Step 11: To find the x-intercepts of the function, we need to set f(x)f(x) to zero and solve for xx.0=(x+2)2−160 = (x+2)^2 - 16
  3. Step 22: We can solve the equation by factoring the right side as a difference of squares:\newline0=[(x+2)+4][(x+2)−4]0 = [(x+2) + 4][(x+2) - 4]
  4. Step 33: This gives us two factors:\newline(x+2)+4=0(x+2) + 4 = 0 or (x+2)−4=0(x+2) - 4 = 0
  5. Step 44: Solving each equation for x gives us the x-intercepts:\newlinex+2+4=0x+2+4=0 leads to x=−6x=-6\newlinex+2−4=0x+2-4=0 leads to x=2x=2
  6. Solution: We have found the two xx-intercepts of the function, which are x=−6x = -6 and x=2x = 2.

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