2. Write the function below in standard form \[ f(x)=4(x+4)^{2}-1 \]

To rewrite the function \( f(x)=4(x+4)^{2}-1 \) in standard form, we first expand the expression. Start by calculating \( (x+4)^2 \): \[ (x+4)^2 = x^2 + 8x + 16 \] Now, substitute this back into the original function: \[ f(x) = 4(x^2 + 8x + 16) - 1 \] Next, distribute the 4: \[ f(x) = 4x^2 + 32x + 64 - 1 \] Finally, combine the constant terms: \[ f(x) = 4x^2 + 32x + 63 \] So, the function in standard form is: \[ f(x) = 4x^2 + 32x + 63 \]