Problem

5. (MGSE9-12.A.CED.2, MGSE9-12.F.BF.1) Which equation is equivalent to \( f(x)= \) \( -3(x-2)^{2}+14 ? \)
A. \( f(x)=-3 x^{2}+2 \)
B. \( f(x)=-3 x^{2}+26 \)
C. \( f(x)=-3 x^{2}-4 x+18 \)
D. \( f(x)=-3 x^{2}+12 x+2 \)

Answer

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Answer

\(f(x) = -3x^{2} + 12x + 2\)

Steps

Step 1 ：Expand the quadratic expression: \(f(x) = -3(x-2)^{2} + 14\)

Step 2 ：\(f(x) = -3(x^{2} - 4x + 4) + 14\)

Step 3 ：\(f(x) = -3x^{2} + 12x + 2\)

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