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Questions: Algebra BusinessCalculus
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Use \(\displaystyle h(x) = 9 x^{2} + 6 x - 7\) to evaluate:
Evaluating the function at \(\displaystyle x = -6\) gives \(\displaystyle f(-6) = 9 (-6)^{2} + 6 (-6) - 7 = 281\).
Evaluating the function at \(\displaystyle x = - 4 x\) gives \(\displaystyle f(- 4 x) = 9 (- 4 x)^{2} + 6 (- 4 x) - 7 = 144 x^{2} - 24 x - 7\).
Evaluating the function at \(\displaystyle x = - t - 3\) gives \(\displaystyle f(- t - 3) = 9 (- t - 3)^{2} + 6 (- t - 3) - 7 = 9 t^{2} + 48 t + 56\).
\begin{question}Use $h(x) = 9 x^{2} + 6 x - 7$ to evaluate:\newline
\begin{tabular}{|l|}\hline
$h(-6)$ \\ \hline
$h(- 4 x)$ \\ \hline
$h(- t - 3)$ \\ \hline
\end{tabular}\newline
\soln{9cm}{Evaluating the function at $x = -6$ gives $f(-6) = 9 (-6)^{2} + 6 (-6) - 7 = 281$.\newline
Evaluating the function at $x = - 4 x$ gives $f(- 4 x) = 9 (- 4 x)^{2} + 6 (- 4 x) - 7 = 144 x^{2} - 24 x - 7$.\newline
Evaluating the function at $x = - t - 3$ gives $f(- t - 3) = 9 (- t - 3)^{2} + 6 (- t - 3) - 7 = 9 t^{2} + 48 t + 56$.\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) = 9 x^{2} + 6 x - 7 " src="/equation_images/%20%5Cdisplaystyle%20h%28x%29%20%3D%209%20x%5E%7B2%7D%20%2B%206%20x%20-%207%20" alt="LaTeX: \displaystyle h(x) = 9 x^{2} + 6 x - 7 " data-equation-content=" \displaystyle h(x) = 9 x^{2} + 6 x - 7 " /> 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) = 9 (-6)^{2} + 6 (-6) - 7 = 281 " src="/equation_images/%20%5Cdisplaystyle%20f%28-6%29%20%3D%209%20%28-6%29%5E%7B2%7D%20%2B%206%20%28-6%29%20-%207%20%3D%20281%20" alt="LaTeX: \displaystyle f(-6) = 9 (-6)^{2} + 6 (-6) - 7 = 281 " data-equation-content=" \displaystyle f(-6) = 9 (-6)^{2} + 6 (-6) - 7 = 281 " /> .<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) = 9 (- 4 x)^{2} + 6 (- 4 x) - 7 = 144 x^{2} - 24 x - 7 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%204%20x%29%20%3D%209%20%28-%204%20x%29%5E%7B2%7D%20%2B%206%20%28-%204%20x%29%20-%207%20%3D%20144%20x%5E%7B2%7D%20-%2024%20x%20-%207%20" alt="LaTeX: \displaystyle f(- 4 x) = 9 (- 4 x)^{2} + 6 (- 4 x) - 7 = 144 x^{2} - 24 x - 7 " data-equation-content=" \displaystyle f(- 4 x) = 9 (- 4 x)^{2} + 6 (- 4 x) - 7 = 144 x^{2} - 24 x - 7 " /> .<br>
Evaluating the function at <img class="equation_image" title=" \displaystyle x = - t - 3 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-%20t%20-%203%20" alt="LaTeX: \displaystyle x = - t - 3 " data-equation-content=" \displaystyle x = - t - 3 " /> gives <img class="equation_image" title=" \displaystyle f(- t - 3) = 9 (- t - 3)^{2} + 6 (- t - 3) - 7 = 9 t^{2} + 48 t + 56 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%20t%20-%203%29%20%3D%209%20%28-%20t%20-%203%29%5E%7B2%7D%20%2B%206%20%28-%20t%20-%203%29%20-%207%20%3D%209%20t%5E%7B2%7D%20%2B%2048%20t%20%2B%2056%20" alt="LaTeX: \displaystyle f(- t - 3) = 9 (- t - 3)^{2} + 6 (- t - 3) - 7 = 9 t^{2} + 48 t + 56 " data-equation-content=" \displaystyle f(- t - 3) = 9 (- t - 3)^{2} + 6 (- t - 3) - 7 = 9 t^{2} + 48 t + 56 " /> .<br>
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