Certainly! Let's complete the square for the function [tex]\( f(x) = x^2 - 12x + 50 \)[/tex].
1. Identify the coefficients:
- The coefficient of [tex]\( x \)[/tex] is [tex]\(-12\)[/tex].
2. Compute [tex]\((\frac{b}{2})^2\)[/tex]:
- For [tex]\( b = -12 \)[/tex],
[tex]\[
\left(\frac{b}{2}\right)^2 = \left(\frac{-12}{2}\right)^2 = (-6)^2 = 36
\][/tex]
3. Rewrite the function by adding and subtracting this square term:
[tex]\[
f(x) = x^2 - 12x + 36 - 36 + 50
\][/tex]
4. Group terms to form a perfect square:
[tex]\[
f(x) = (x^2 - 12x + 36) + (-36 + 50)
\][/tex]
5. Rewrite the perfect square and simplify the constant term:
[tex]\[
f(x) = (x - 6)^2 + 14
\][/tex]
Therefore, the function [tex]\( f(x) \)[/tex] rewritten by completing the square is:
[tex]\[
f(x) = (x - 6)^2 + 14
\][/tex]
So we have:
[tex]\[
f(x) = (x - 6)^2 + 14
\][/tex]
You can now see the function in its completed square form, indicating how the quadratic function can be expressed as a squared binomial plus a constant.
