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Find g(x)g(x), where g(x)g(x) is the reflection across the x-axis of f(x)=−6(x−7)2+2f(x) = -6(x - 7)^2 + 2.\newlineChoices:\newline(A) g(x)=6(x−7)2−2g(x) = 6(x - 7)^2 - 2\newline(B) g(x)=−6(x+7)2+2g(x) = -6(x + 7)^2 + 2\newline(C) g(x)=−6(x−7)2−2g(x) = -6(x - 7)^2 - 2\newline(D) g(x)=6(x+7)2−2g(x) = 6(x + 7)^2 - 2

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Q. Find g(x)g(x), where g(x)g(x) is the reflection across the x-axis of f(x)=−6(x−7)2+2f(x) = -6(x - 7)^2 + 2.\newlineChoices:\newline(A) g(x)=6(x−7)2−2g(x) = 6(x - 7)^2 - 2\newline(B) g(x)=−6(x+7)2+2g(x) = -6(x + 7)^2 + 2\newline(C) g(x)=−6(x−7)2−2g(x) = -6(x - 7)^2 - 2\newline(D) g(x)=6(x+7)2−2g(x) = 6(x + 7)^2 - 2
  1. Multiply yy-values by −1-1: To reflect a function across the xx-axis, we need to multiply the yy-values (output of the function) by −1-1. This means we will change the sign of the entire function f(x)f(x).
  2. Modify original function: The original function is f(x)=−6(x−7)2+2f(x) = -6(x - 7)^2 + 2. To reflect it across the x-axis, we multiply by −1-1 to get g(x)=−1×[−6(x−7)2+2]g(x) = -1 \times [-6(x - 7)^2 + 2].
  3. Distribute −1-1 across function: Distribute the −1-1 across the function to change the signs: g(x)=−1×[–6(x–7)2]+−1×[2]g(x) = -1 \times [–6(x – 7)^2] + -1 \times [2].
  4. Simplify the expression: Simplify the expression: g(x)=6(x–7)2−2g(x) = 6(x – 7)^2 - 2.
  5. Choose correct option: Now we choose the correct option that matches our result. The correct option is g(x)=6(x–7)2–2g(x) = 6(x – 7)^2 – 2.

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