Question

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

Answer 1

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:
\[
f(x) = 3x^2 + 42x + 145
\]