Pregunta
Rewrite the function by completing the square. \( f(x)=x^{2}-12 x-29 \) \( f(x)=(x+\square)^{2}+\square \)
Ask by Chadwick Macdonald. in the United States
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\( f(x) = (x - 6)^2 - 65 \)
Solución
To complete the square for the function \( f(x) = x^{2} - 12x - 29 \), follow these steps:
1. **Identify the coefficients:**
- The coefficient of \( x \) is \(-12\).
2. **Half the coefficient of \( x \) and square it:**
- Half of \(-12\) is \(-6\).
- Squaring \(-6\) gives \( 36 \).
3. **Rewrite the function by adding and subtracting this square:**
\[
f(x) = x^{2} - 12x + 36 - 36 - 29
\]
\[
f(x) = (x - 6)^{2} - 65
\]
So, the function rewritten by completing the square is:
\[
f(x) = (x - 6)^{2} - 65
\]
**Filled in the blanks:**
\[
f(x) = (x - 6)^{2} - 65
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
To complete the square for the function \( f(x)=x^{2}-12 x-29 \), we start by focusing on the quadratic part: \( x^2 - 12x \). We take half of the coefficient of \( x \), which is -12, leading to -6, and then square it, getting 36. Now, we rewrite the function as follows: \[ f(x) = (x^2 - 12x + 36) - 36 - 29 \] \[ f(x) = (x - 6)^2 - 65 \] Thus, we can express it in the completed square form: \[ f(x) = (x - 6)^2 - 65 \] So, filling in the squares, we have: \( f(x)=(x-6)^{2}-65 \)
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