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Questions: Algebra BusinessCalculus
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Use \(\displaystyle g(x) = - 2 x^{2} - 6 x + 4\) to evaluate:
Evaluating the function at \(\displaystyle x = -6\) gives \(\displaystyle f(-6) = - 2 (-6)^{2} - 6 (-6) + 4 = -32\).
Evaluating the function at \(\displaystyle x = - x\) gives \(\displaystyle f(- x) = - 2 (- x)^{2} - 6 (- x) + 4 = - 2 x^{2} + 6 x + 4\).
Evaluating the function at \(\displaystyle x = - t - 2\) gives \(\displaystyle f(- t - 2) = - 2 (- t - 2)^{2} - 6 (- t - 2) + 4 = - 2 t^{2} - 2 t + 8\).
\begin{question}Use $g(x) = - 2 x^{2} - 6 x + 4$ to evaluate:\newline
\begin{tabular}{|l|}\hline
$g(-6)$ \\ \hline
$g(- x)$ \\ \hline
$g(- t - 2)$ \\ \hline
\end{tabular}\newline
\soln{9cm}{Evaluating the function at $x = -6$ gives $f(-6) = - 2 (-6)^{2} - 6 (-6) + 4 = -32$.\newline
Evaluating the function at $x = - x$ gives $f(- x) = - 2 (- x)^{2} - 6 (- x) + 4 = - 2 x^{2} + 6 x + 4$.\newline
Evaluating the function at $x = - t - 2$ gives $f(- t - 2) = - 2 (- t - 2)^{2} - 6 (- t - 2) + 4 = - 2 t^{2} - 2 t + 8$.\newline
}
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Use <img class="equation_image" title=" \displaystyle g(x) = - 2 x^{2} - 6 x + 4 " src="/equation_images/%20%5Cdisplaystyle%20g%28x%29%20%3D%20-%202%20x%5E%7B2%7D%20-%206%20x%20%2B%204%20" alt="LaTeX: \displaystyle g(x) = - 2 x^{2} - 6 x + 4 " data-equation-content=" \displaystyle g(x) = - 2 x^{2} - 6 x + 4 " /> to evaluate:<br>
</p> </p><p> <p>Evaluating the function at <img class="equation_image" title=" \displaystyle x = -6 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-6%20" alt="LaTeX: \displaystyle x = -6 " data-equation-content=" \displaystyle x = -6 " /> gives <img class="equation_image" title=" \displaystyle f(-6) = - 2 (-6)^{2} - 6 (-6) + 4 = -32 " src="/equation_images/%20%5Cdisplaystyle%20f%28-6%29%20%3D%20-%202%20%28-6%29%5E%7B2%7D%20-%206%20%28-6%29%20%2B%204%20%3D%20-32%20" alt="LaTeX: \displaystyle f(-6) = - 2 (-6)^{2} - 6 (-6) + 4 = -32 " data-equation-content=" \displaystyle f(-6) = - 2 (-6)^{2} - 6 (-6) + 4 = -32 " /> .<br>
Evaluating the function at <img class="equation_image" title=" \displaystyle x = - x " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-%20x%20" alt="LaTeX: \displaystyle x = - x " data-equation-content=" \displaystyle x = - x " /> gives <img class="equation_image" title=" \displaystyle f(- x) = - 2 (- x)^{2} - 6 (- x) + 4 = - 2 x^{2} + 6 x + 4 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%20x%29%20%3D%20-%202%20%28-%20x%29%5E%7B2%7D%20-%206%20%28-%20x%29%20%2B%204%20%3D%20-%202%20x%5E%7B2%7D%20%2B%206%20x%20%2B%204%20" alt="LaTeX: \displaystyle f(- x) = - 2 (- x)^{2} - 6 (- x) + 4 = - 2 x^{2} + 6 x + 4 " data-equation-content=" \displaystyle f(- x) = - 2 (- x)^{2} - 6 (- x) + 4 = - 2 x^{2} + 6 x + 4 " /> .<br>
Evaluating the function at <img class="equation_image" title=" \displaystyle x = - t - 2 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-%20t%20-%202%20" alt="LaTeX: \displaystyle x = - t - 2 " data-equation-content=" \displaystyle x = - t - 2 " /> gives <img class="equation_image" title=" \displaystyle f(- t - 2) = - 2 (- t - 2)^{2} - 6 (- t - 2) + 4 = - 2 t^{2} - 2 t + 8 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%20t%20-%202%29%20%3D%20-%202%20%28-%20t%20-%202%29%5E%7B2%7D%20-%206%20%28-%20t%20-%202%29%20%2B%204%20%3D%20-%202%20t%5E%7B2%7D%20-%202%20t%20%2B%208%20" alt="LaTeX: \displaystyle f(- t - 2) = - 2 (- t - 2)^{2} - 6 (- t - 2) + 4 = - 2 t^{2} - 2 t + 8 " data-equation-content=" \displaystyle f(- t - 2) = - 2 (- t - 2)^{2} - 6 (- t - 2) + 4 = - 2 t^{2} - 2 t + 8 " /> .<br>
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