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Questions: Algebra BusinessCalculus
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Use \(\displaystyle h(x) = 5 x^{2} + 8 x + 2\) to evaluate:
Evaluating the function at \(\displaystyle x = 4\) gives \(\displaystyle f(4) = 5 (4)^{2} + 8 (4) + 2 = 114\).
Evaluating the function at \(\displaystyle x = - 4 x\) gives \(\displaystyle f(- 4 x) = 5 (- 4 x)^{2} + 8 (- 4 x) + 2 = 80 x^{2} - 32 x + 2\).
Evaluating the function at \(\displaystyle x = 3 - t\) gives \(\displaystyle f(3 - t) = 5 (3 - t)^{2} + 8 (3 - t) + 2 = 5 t^{2} - 38 t + 71\).
\begin{question}Use $h(x) = 5 x^{2} + 8 x + 2$ to evaluate:\newline
\begin{tabular}{|l|}\hline
$h(4)$ \\ \hline
$h(- 4 x)$ \\ \hline
$h(3 - t)$ \\ \hline
\end{tabular}\newline
\soln{9cm}{Evaluating the function at $x = 4$ gives $f(4) = 5 (4)^{2} + 8 (4) + 2 = 114$.\newline
Evaluating the function at $x = - 4 x$ gives $f(- 4 x) = 5 (- 4 x)^{2} + 8 (- 4 x) + 2 = 80 x^{2} - 32 x + 2$.\newline
Evaluating the function at $x = 3 - t$ gives $f(3 - t) = 5 (3 - t)^{2} + 8 (3 - t) + 2 = 5 t^{2} - 38 t + 71$.\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) = 5 x^{2} + 8 x + 2 " src="/equation_images/%20%5Cdisplaystyle%20h%28x%29%20%3D%205%20x%5E%7B2%7D%20%2B%208%20x%20%2B%202%20" alt="LaTeX: \displaystyle h(x) = 5 x^{2} + 8 x + 2 " data-equation-content=" \displaystyle h(x) = 5 x^{2} + 8 x + 2 " /> to evaluate:<br>
</p> </p><p> <p>Evaluating the function at <img class="equation_image" title=" \displaystyle x = 4 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%204%20" alt="LaTeX: \displaystyle x = 4 " data-equation-content=" \displaystyle x = 4 " /> gives <img class="equation_image" title=" \displaystyle f(4) = 5 (4)^{2} + 8 (4) + 2 = 114 " src="/equation_images/%20%5Cdisplaystyle%20f%284%29%20%3D%205%20%284%29%5E%7B2%7D%20%2B%208%20%284%29%20%2B%202%20%3D%20114%20" alt="LaTeX: \displaystyle f(4) = 5 (4)^{2} + 8 (4) + 2 = 114 " data-equation-content=" \displaystyle f(4) = 5 (4)^{2} + 8 (4) + 2 = 114 " /> .<br>
Evaluating the function at <img class="equation_image" title=" \displaystyle x = - 4 x " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-%204%20x%20" alt="LaTeX: \displaystyle x = - 4 x " data-equation-content=" \displaystyle x = - 4 x " /> gives <img class="equation_image" title=" \displaystyle f(- 4 x) = 5 (- 4 x)^{2} + 8 (- 4 x) + 2 = 80 x^{2} - 32 x + 2 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%204%20x%29%20%3D%205%20%28-%204%20x%29%5E%7B2%7D%20%2B%208%20%28-%204%20x%29%20%2B%202%20%3D%2080%20x%5E%7B2%7D%20-%2032%20x%20%2B%202%20" alt="LaTeX: \displaystyle f(- 4 x) = 5 (- 4 x)^{2} + 8 (- 4 x) + 2 = 80 x^{2} - 32 x + 2 " data-equation-content=" \displaystyle f(- 4 x) = 5 (- 4 x)^{2} + 8 (- 4 x) + 2 = 80 x^{2} - 32 x + 2 " /> .<br>
Evaluating the function at <img class="equation_image" title=" \displaystyle x = 3 - t " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%203%20-%20t%20" alt="LaTeX: \displaystyle x = 3 - t " data-equation-content=" \displaystyle x = 3 - t " /> gives <img class="equation_image" title=" \displaystyle f(3 - t) = 5 (3 - t)^{2} + 8 (3 - t) + 2 = 5 t^{2} - 38 t + 71 " src="/equation_images/%20%5Cdisplaystyle%20f%283%20-%20t%29%20%3D%205%20%283%20-%20t%29%5E%7B2%7D%20%2B%208%20%283%20-%20t%29%20%2B%202%20%3D%205%20t%5E%7B2%7D%20-%2038%20t%20%2B%2071%20" alt="LaTeX: \displaystyle f(3 - t) = 5 (3 - t)^{2} + 8 (3 - t) + 2 = 5 t^{2} - 38 t + 71 " data-equation-content=" \displaystyle f(3 - t) = 5 (3 - t)^{2} + 8 (3 - t) + 2 = 5 t^{2} - 38 t + 71 " /> .<br>
</p> </p>