## MAT 101 Online Stewart Section 4.1: Quadratic Functions and Models

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• Started 1 year ago by lee

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1. lee
Key Master

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 $f(x)=2(x-3)^2+5$.

Posted 1 year ago #