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In this problem, we will explore quadratic functions and their roots.
\begin{enumerate}
    \item Consider the function $f(x) = x^2 + 4x + c$. For what values of $c$ does this functions have no roots? A double root? Two distinct roots?
    \item Why do your answers to the first part make sense? Consider the graph of the function $g(x) = x^2 + 4x$. What are we doing to the graph of this function by changing $c$?
    \item Now, consider the function $f(x) = x^2 + bx + 4$. For what values of $b$ do we have no roots? A double root? Two distinct roots?
    \item What about the function $f(x) = x^2 + bx - 4$? Answer the same questions here.
    
\end{enumerate}
    
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