Question
2. Write the function below in standard form \[ f(x)=4(x+4)^{2}-1 \]
Ask by Barber Knight. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f(x) = 4x^{2} + 32x + 63 \)
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Beyond the Answer
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: \[ f(x) = 4x^2 + 32x + 63 \]
