how do i find the minimum value or maximum value of function
x^2-12x+9?
Rewrite it in vertex form:
$\displaystyle y = a(x - h)^2 + k$.
If the leading coefficient is positive, then the vertex (h, k) is the minimum point; if the leading coefficient is negative, then the vertex (h, k) is the maximum point.
So, we complete the square to rewrite the equation in vertex form:
$\displaystyle x^2-12x+9$
$\displaystyle \begin{aligned}
&= x^2 - 12x \;{\color{red}+\;36}\;+ 9\; {\color{red}-\;36} \\
&= (x - 6)^2 - 27
\end{aligned}$
The leading coefficient was positive (a = 1), so the point (6, -27) is the minimum of the parabola.
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