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Questions: Algebra BusinessCalculus
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Use \(\displaystyle f(x) = - 7 x^{2} - x + 9\) to evaluate:
Evaluating the function at \(\displaystyle x = 9\) gives \(\displaystyle f(9) = - 7 (9)^{2} - (9) + 9 = -567\).
Evaluating the function at \(\displaystyle x = - 3 x\) gives \(\displaystyle f(- 3 x) = - 7 (- 3 x)^{2} - (- 3 x) + 9 = - 63 x^{2} + 3 x + 9\).
Evaluating the function at \(\displaystyle x = 3 - t\) gives \(\displaystyle f(3 - t) = - 7 (3 - t)^{2} - (3 - t) + 9 = - 7 t^{2} + 43 t - 57\).
\begin{question}Use $f(x) = - 7 x^{2} - x + 9$ to evaluate:\newline
\begin{tabular}{|l|}\hline
$f(9)$ \\ \hline
$f(- 3 x)$ \\ \hline
$f(3 - t)$ \\ \hline
\end{tabular}\newline
\soln{9cm}{Evaluating the function at $x = 9$ gives $f(9) = - 7 (9)^{2} - (9) + 9 = -567$.\newline
Evaluating the function at $x = - 3 x$ gives $f(- 3 x) = - 7 (- 3 x)^{2} - (- 3 x) + 9 = - 63 x^{2} + 3 x + 9$.\newline
Evaluating the function at $x = 3 - t$ gives $f(3 - t) = - 7 (3 - t)^{2} - (3 - t) + 9 = - 7 t^{2} + 43 t - 57$.\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 f(x) = - 7 x^{2} - x + 9 " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20-%207%20x%5E%7B2%7D%20-%20x%20%2B%209%20" alt="LaTeX: \displaystyle f(x) = - 7 x^{2} - x + 9 " data-equation-content=" \displaystyle f(x) = - 7 x^{2} - x + 9 " /> 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%209%20" alt="LaTeX: \displaystyle x = 9 " data-equation-content=" \displaystyle x = 9 " /> gives <img class="equation_image" title=" \displaystyle f(9) = - 7 (9)^{2} - (9) + 9 = -567 " src="/equation_images/%20%5Cdisplaystyle%20f%289%29%20%3D%20-%207%20%289%29%5E%7B2%7D%20-%20%289%29%20%2B%209%20%3D%20-567%20" alt="LaTeX: \displaystyle f(9) = - 7 (9)^{2} - (9) + 9 = -567 " data-equation-content=" \displaystyle f(9) = - 7 (9)^{2} - (9) + 9 = -567 " /> .<br>
Evaluating the function at <img class="equation_image" title=" \displaystyle x = - 3 x " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-%203%20x%20" alt="LaTeX: \displaystyle x = - 3 x " data-equation-content=" \displaystyle x = - 3 x " /> gives <img class="equation_image" title=" \displaystyle f(- 3 x) = - 7 (- 3 x)^{2} - (- 3 x) + 9 = - 63 x^{2} + 3 x + 9 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%203%20x%29%20%3D%20-%207%20%28-%203%20x%29%5E%7B2%7D%20-%20%28-%203%20x%29%20%2B%209%20%3D%20-%2063%20x%5E%7B2%7D%20%2B%203%20x%20%2B%209%20" alt="LaTeX: \displaystyle f(- 3 x) = - 7 (- 3 x)^{2} - (- 3 x) + 9 = - 63 x^{2} + 3 x + 9 " data-equation-content=" \displaystyle f(- 3 x) = - 7 (- 3 x)^{2} - (- 3 x) + 9 = - 63 x^{2} + 3 x + 9 " /> .<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) = - 7 (3 - t)^{2} - (3 - t) + 9 = - 7 t^{2} + 43 t - 57 " src="/equation_images/%20%5Cdisplaystyle%20f%283%20-%20t%29%20%3D%20-%207%20%283%20-%20t%29%5E%7B2%7D%20-%20%283%20-%20t%29%20%2B%209%20%3D%20-%207%20t%5E%7B2%7D%20%2B%2043%20t%20-%2057%20" alt="LaTeX: \displaystyle f(3 - t) = - 7 (3 - t)^{2} - (3 - t) + 9 = - 7 t^{2} + 43 t - 57 " data-equation-content=" \displaystyle f(3 - t) = - 7 (3 - t)^{2} - (3 - t) + 9 = - 7 t^{2} + 43 t - 57 " /> .<br>
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