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f(x)=(x+6)^(2)-16 At what values of x does the graph of the function intersect the x-axis? Choose 1 answer: (A) x=-2,x=10 (B) x=2,x=-10 (c) x=-2,x=-10 (D) f(x) does not intersect the x-axis.

f(x)=(x+6)2−16 f(x)=(x+6)^{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=10 x=-2, x=10 \newline(B) x=2,x=−10 x=2, x=-10 \newline(C) x=−2,x=−10 x=-2, x=-10 \newline(D) f(x) f(x) does not intersect the x x -axis.

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Q. f(x)=(x+6)2−16 f(x)=(x+6)^{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=10 x=-2, x=10 \newline(B) x=2,x=−10 x=2, x=-10 \newline(C) x=−2,x=−10 x=-2, x=-10 \newline(D) f(x) f(x) does not intersect the x x -axis.
  1. Set f(x)f(x) to zero: To find the xx-intercepts of the graph of the function, we need to set f(x)f(x) to zero and solve for xx.\newlinef(x)=(x+6)2−16=0f(x) = (x+6)^2 - 16 = 0
  2. Solve for x: Now we solve the equation (x+6)2−16=0(x+6)^2 - 16 = 0. Add 1616 to both sides to isolate the squared term. (x+6)2=16(x+6)^2 = 16
  3. Isolate squared term: Take the square root of both sides to solve for xx.(x+6)2=±16\sqrt{(x+6)^2} = \pm\sqrt{16}x+6=±4x + 6 = \pm4
  4. Take square root: Now we solve for xx by subtracting 66 from both sides of each equation.\newlinex+6−6=4−6x + 6 - 6 = 4 - 6 and x+6−6=−4−6x + 6 - 6 = -4 - 6\newlinex=−2x = -2 and x=−10x = -10

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