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Questions: Algebra BusinessCalculus
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Use \(\displaystyle g(x) = - 8 x^{2} + 9 x + 5\) to evaluate:
Evaluating the function at \(\displaystyle x = -9\) gives \(\displaystyle f(-9) = - 8 (-9)^{2} + 9 (-9) + 5 = -724\).
Evaluating the function at \(\displaystyle x = - x\) gives \(\displaystyle f(- x) = - 8 (- x)^{2} + 9 (- x) + 5 = - 8 x^{2} - 9 x + 5\).
Evaluating the function at \(\displaystyle x = 2 - t\) gives \(\displaystyle f(2 - t) = - 8 (2 - t)^{2} + 9 (2 - t) + 5 = - 8 t^{2} + 23 t - 9\).
\begin{question}Use $g(x) = - 8 x^{2} + 9 x + 5$ to evaluate:\newline
\begin{tabular}{|l|}\hline
$g(-9)$ \\ \hline
$g(- x)$ \\ \hline
$g(2 - t)$ \\ \hline
\end{tabular}\newline
\soln{9cm}{Evaluating the function at $x = -9$ gives $f(-9) = - 8 (-9)^{2} + 9 (-9) + 5 = -724$.\newline
Evaluating the function at $x = - x$ gives $f(- x) = - 8 (- x)^{2} + 9 (- x) + 5 = - 8 x^{2} - 9 x + 5$.\newline
Evaluating the function at $x = 2 - t$ gives $f(2 - t) = - 8 (2 - t)^{2} + 9 (2 - t) + 5 = - 8 t^{2} + 23 t - 9$.\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) = - 8 x^{2} + 9 x + 5 " src="/equation_images/%20%5Cdisplaystyle%20g%28x%29%20%3D%20-%208%20x%5E%7B2%7D%20%2B%209%20x%20%2B%205%20" alt="LaTeX: \displaystyle g(x) = - 8 x^{2} + 9 x + 5 " data-equation-content=" \displaystyle g(x) = - 8 x^{2} + 9 x + 5 " /> to evaluate:<br>
</p> </p><p> <p>Evaluating the function at <img class="equation_image" title=" \displaystyle x = -9 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-9%20" alt="LaTeX: \displaystyle x = -9 " data-equation-content=" \displaystyle x = -9 " /> gives <img class="equation_image" title=" \displaystyle f(-9) = - 8 (-9)^{2} + 9 (-9) + 5 = -724 " src="/equation_images/%20%5Cdisplaystyle%20f%28-9%29%20%3D%20-%208%20%28-9%29%5E%7B2%7D%20%2B%209%20%28-9%29%20%2B%205%20%3D%20-724%20" alt="LaTeX: \displaystyle f(-9) = - 8 (-9)^{2} + 9 (-9) + 5 = -724 " data-equation-content=" \displaystyle f(-9) = - 8 (-9)^{2} + 9 (-9) + 5 = -724 " /> .<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) = - 8 (- x)^{2} + 9 (- x) + 5 = - 8 x^{2} - 9 x + 5 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%20x%29%20%3D%20-%208%20%28-%20x%29%5E%7B2%7D%20%2B%209%20%28-%20x%29%20%2B%205%20%3D%20-%208%20x%5E%7B2%7D%20-%209%20x%20%2B%205%20" alt="LaTeX: \displaystyle f(- x) = - 8 (- x)^{2} + 9 (- x) + 5 = - 8 x^{2} - 9 x + 5 " data-equation-content=" \displaystyle f(- x) = - 8 (- x)^{2} + 9 (- x) + 5 = - 8 x^{2} - 9 x + 5 " /> .<br>
Evaluating the function at <img class="equation_image" title=" \displaystyle x = 2 - t " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%202%20-%20t%20" alt="LaTeX: \displaystyle x = 2 - t " data-equation-content=" \displaystyle x = 2 - t " /> gives <img class="equation_image" title=" \displaystyle f(2 - t) = - 8 (2 - t)^{2} + 9 (2 - t) + 5 = - 8 t^{2} + 23 t - 9 " src="/equation_images/%20%5Cdisplaystyle%20f%282%20-%20t%29%20%3D%20-%208%20%282%20-%20t%29%5E%7B2%7D%20%2B%209%20%282%20-%20t%29%20%2B%205%20%3D%20-%208%20t%5E%7B2%7D%20%2B%2023%20t%20-%209%20" alt="LaTeX: \displaystyle f(2 - t) = - 8 (2 - t)^{2} + 9 (2 - t) + 5 = - 8 t^{2} + 23 t - 9 " data-equation-content=" \displaystyle f(2 - t) = - 8 (2 - t)^{2} + 9 (2 - t) + 5 = - 8 t^{2} + 23 t - 9 " /> .<br>
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