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f(x)=(x-4)^(2)-16 At what values of x does the graph of the function intersect the x-axis? Choose 1 answer: (A) x=8,x=0 (B) x=-8,x=0 (c) x=8,x=-8 (D) f(x) does not intersect the x-axis.

f(x)=(x−4)2−16 f(x)=(x-4)^{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=8,x=0 x=8, x=0 \newline(B) x=−8,x=0 x=-8, x=0 \newline(C) x=8,x=−8 x=8, x=-8 \newline(D) f(x) f(x) does not intersect the x x -axis.

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Q. f(x)=(x−4)2−16 f(x)=(x-4)^{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=8,x=0 x=8, x=0 \newline(B) x=−8,x=0 x=-8, x=0 \newline(C) x=8,x=−8 x=8, x=-8 \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 where the function f(x)f(x) intersects the xx-axis. The xx-axis is where the value of the function f(x)f(x) is zero.
  2. Setting the Equation: Set the function equal to zero to find the x-intercepts.\newline0=(x−4)2−160 = (x-4)^{2} - 16
  3. Solving the Equation: Solve the equation for xx.\newlineAdd 1616 to both sides of the equation to isolate the squared term.\newline(x−4)2=16(x-4)^{2} = 16
  4. Taking the Square Root: Take the square root of both sides.\newline(x−4)2=±16\sqrt{(x-4)^{2}} = \pm\sqrt{16}\newlinex−4=±4x - 4 = \pm4
  5. Final Solution: Solve for xx.x=4+4 or x=4−4x = 4 + 4 \text{ or } x = 4 - 4x=8 or x=0x = 8 \text{ or } x = 0

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