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Questions: Algebra BusinessCalculus
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Use \(\displaystyle h(x) = - 8 x^{2} - 7 x - 1\) to evaluate:
Evaluating the function at \(\displaystyle x = -5\) gives \(\displaystyle f(-5) = - 8 (-5)^{2} - 7 (-5) - 1 = -166\).
Evaluating the function at \(\displaystyle x = - 2 x\) gives \(\displaystyle f(- 2 x) = - 8 (- 2 x)^{2} - 7 (- 2 x) - 1 = - 32 x^{2} + 14 x - 1\).
Evaluating the function at \(\displaystyle x = - t - 1\) gives \(\displaystyle f(- t - 1) = - 8 (- t - 1)^{2} - 7 (- t - 1) - 1 = - 8 t^{2} - 9 t - 2\).
\begin{question}Use $h(x) = - 8 x^{2} - 7 x - 1$ to evaluate:\newline
\begin{tabular}{|l|}\hline
$h(-5)$ \\ \hline
$h(- 2 x)$ \\ \hline
$h(- t - 1)$ \\ \hline
\end{tabular}\newline
\soln{9cm}{Evaluating the function at $x = -5$ gives $f(-5) = - 8 (-5)^{2} - 7 (-5) - 1 = -166$.\newline
Evaluating the function at $x = - 2 x$ gives $f(- 2 x) = - 8 (- 2 x)^{2} - 7 (- 2 x) - 1 = - 32 x^{2} + 14 x - 1$.\newline
Evaluating the function at $x = - t - 1$ gives $f(- t - 1) = - 8 (- t - 1)^{2} - 7 (- t - 1) - 1 = - 8 t^{2} - 9 t - 2$.\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 h(x) = - 8 x^{2} - 7 x - 1 " src="/equation_images/%20%5Cdisplaystyle%20h%28x%29%20%3D%20-%208%20x%5E%7B2%7D%20-%207%20x%20-%201%20" alt="LaTeX: \displaystyle h(x) = - 8 x^{2} - 7 x - 1 " data-equation-content=" \displaystyle h(x) = - 8 x^{2} - 7 x - 1 " /> to evaluate:<br>
</p> </p><p> <p>Evaluating the function at <img class="equation_image" title=" \displaystyle x = -5 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-5%20" alt="LaTeX: \displaystyle x = -5 " data-equation-content=" \displaystyle x = -5 " /> gives <img class="equation_image" title=" \displaystyle f(-5) = - 8 (-5)^{2} - 7 (-5) - 1 = -166 " src="/equation_images/%20%5Cdisplaystyle%20f%28-5%29%20%3D%20-%208%20%28-5%29%5E%7B2%7D%20-%207%20%28-5%29%20-%201%20%3D%20-166%20" alt="LaTeX: \displaystyle f(-5) = - 8 (-5)^{2} - 7 (-5) - 1 = -166 " data-equation-content=" \displaystyle f(-5) = - 8 (-5)^{2} - 7 (-5) - 1 = -166 " /> .<br>
Evaluating the function at <img class="equation_image" title=" \displaystyle x = - 2 x " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-%202%20x%20" alt="LaTeX: \displaystyle x = - 2 x " data-equation-content=" \displaystyle x = - 2 x " /> gives <img class="equation_image" title=" \displaystyle f(- 2 x) = - 8 (- 2 x)^{2} - 7 (- 2 x) - 1 = - 32 x^{2} + 14 x - 1 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%202%20x%29%20%3D%20-%208%20%28-%202%20x%29%5E%7B2%7D%20-%207%20%28-%202%20x%29%20-%201%20%3D%20-%2032%20x%5E%7B2%7D%20%2B%2014%20x%20-%201%20" alt="LaTeX: \displaystyle f(- 2 x) = - 8 (- 2 x)^{2} - 7 (- 2 x) - 1 = - 32 x^{2} + 14 x - 1 " data-equation-content=" \displaystyle f(- 2 x) = - 8 (- 2 x)^{2} - 7 (- 2 x) - 1 = - 32 x^{2} + 14 x - 1 " /> .<br>
Evaluating the function at <img class="equation_image" title=" \displaystyle x = - t - 1 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-%20t%20-%201%20" alt="LaTeX: \displaystyle x = - t - 1 " data-equation-content=" \displaystyle x = - t - 1 " /> gives <img class="equation_image" title=" \displaystyle f(- t - 1) = - 8 (- t - 1)^{2} - 7 (- t - 1) - 1 = - 8 t^{2} - 9 t - 2 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%20t%20-%201%29%20%3D%20-%208%20%28-%20t%20-%201%29%5E%7B2%7D%20-%207%20%28-%20t%20-%201%29%20-%201%20%3D%20-%208%20t%5E%7B2%7D%20-%209%20t%20-%202%20" alt="LaTeX: \displaystyle f(- t - 1) = - 8 (- t - 1)^{2} - 7 (- t - 1) - 1 = - 8 t^{2} - 9 t - 2 " data-equation-content=" \displaystyle f(- t - 1) = - 8 (- t - 1)^{2} - 7 (- t - 1) - 1 = - 8 t^{2} - 9 t - 2 " /> .<br>
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