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here as a quadratic function f in vertex form f(x)=3(x+7)^2-2 select the equation that repersents f in stander form f(x)=9x^2+126x+439 f(x)=3^2+14+47 f(x)=9x^2+63+435 f(x)=3x^2+42x+145

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To convert the quadratic function given in vertex form \( f(x) = 3(x + 7)^2 - 2 \) to standard form, we need to expand the expression.

  1. Start by expanding the squared term: \[ (x + 7)^2 = x^2 + 14x + 49 \]

  2. Now substitute this back into the function: \[ f(x) = 3(x^2 + 14x + 49) - 2 \]

  3. Distribute the 3: \[ f(x) = 3x^2 + 42x + 147 - 2 \]

  4. Combine the constant terms: \[ f(x) = 3x^2 + 42x + 145 \]

So the standard form of the function is: \[ f(x) = 3x^2 + 42x + 145 \]

Among the choices presented, the equation that represents \( f \) in standard form is: \[ f(x) = 3x^2 + 42x + 145 \]