In Stewart's textbook, you are instructed to rewrite a given quadratic function $y=ax^2+bx+c$ in the standard form $y=a(x-k)^2+h$ by completing the square. However, it is unnecessary. All you have to know is the formula for the $x$-coordinate of the vertex $(k,h)$ which is $k=-\frac{b}{2a}$. Note that this formula actually comes from completing the square. The $y$-coordinate of the vertex is then found by calculating $h=f(k)$.

* Example.* Express $f(x)=2x^2-12x+23$ in standard form. (Example 1 on page 189.)

**Solution.** $k=-\frac{b}{2a}=-\frac{-12}{2\cdot 2}=3$ and

\begin{align*}

h&=f(k)\\

&=f(3)\\

&=2(3)^2-12(3)+23\\

&=5.

\end{align*}

Hence, in standard form $f(x)=2(x-3)^2+5$.