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Problems PreCal 1508 PLTL Workshop, September 14, 2011 \\
PL: Alex Knaust, Lecturer: Yi-Yu Liao
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\begin{enumerate}
\item Graph the following quadratic functions and find their vertex and $x$-intercepts.
\begin{enumerate}
\item $f(x) = 2x^2 + 4x + 7$
\item $g(x) = 3(x - 4)^2 + 3$
\end{enumerate}
\item Use long division to divide $f(x) = x^5 - 2x^4 +x^3 - 4x^2 + 4x$ by $q(x) = x^2 + x + 2$.
\item Find the value of $b$ such that the function has the given minimum or maximum value.
\begin{enumerate}
\item $f(x) = x^2 + bx +26$; Minimum value $10$
\end{enumerate}
\item What is the discriminant of $f(x) = qx^2 + rx +s$ and what can it tell you about $f$?
\item Determine through Long Division if $3$ is a root of $f(x) = x^3 + 6x^2 - 25x - 6$.
\item Is the vertex of a quadratic function and one other point enough to uniquely determine it? Explain.
\item Create a version of the division theorem for positive Integers. What will you use instead of \emph{degree}?
\item If $f(x)$ is a polynomial of degree $n$ and $g$ is a polynomial of degree $m$ what is the degree
of $f + g$? of $f \cdot g$?
\item If $f$ is an odd function, is $f \circ f$ also odd?
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