Question
Write f(x)=-3(x+1)^2-4 in standard form
Answers
GPT-4o mini
To rewrite the function \( f(x) = -3(x + 1)^2 - 4 \) in standard form, we will expand it:
1. Start with the expression:
\[ f(x) = -3(x + 1)^2 - 4 \]
2. First, expand \( (x + 1)^2 \):
\[ (x + 1)^2 = x^2 + 2x + 1 \]
3. Substitute this back into the function:
\[ f(x) = -3(x^2 + 2x + 1) - 4 \]
4. Distribute the -3:
\[ f(x) = -3x^2 - 6x - 3 - 4 \]
5. Now combine the constant terms:
\[ -3 - 4 = -7 \]
6. Thus, the standard form of the function is:
\[ f(x) = -3x^2 - 6x - 7 \]
So, the standard form of the function is:
\[
f(x) = -3x^2 - 6x - 7
\]
1. Start with the expression:
\[ f(x) = -3(x + 1)^2 - 4 \]
2. First, expand \( (x + 1)^2 \):
\[ (x + 1)^2 = x^2 + 2x + 1 \]
3. Substitute this back into the function:
\[ f(x) = -3(x^2 + 2x + 1) - 4 \]
4. Distribute the -3:
\[ f(x) = -3x^2 - 6x - 3 - 4 \]
5. Now combine the constant terms:
\[ -3 - 4 = -7 \]
6. Thus, the standard form of the function is:
\[ f(x) = -3x^2 - 6x - 7 \]
So, the standard form of the function is:
\[
f(x) = -3x^2 - 6x - 7
\]