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Questions: Algebra BusinessCalculus
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Use \(\displaystyle h(x) = - x^{2} + 4 x - 1\) to evaluate:
Evaluating the function at \(\displaystyle x = -4\) gives \(\displaystyle f(-4) = - (-4)^{2} + 4 (-4) - 1 = -33\).
Evaluating the function at \(\displaystyle x = - x\) gives \(\displaystyle f(- x) = - (- x)^{2} + 4 (- x) - 1 = - x^{2} - 4 x - 1\).
Evaluating the function at \(\displaystyle x = - t - 2\) gives \(\displaystyle f(- t - 2) = - (- t - 2)^{2} + 4 (- t - 2) - 1 = - t^{2} - 8 t - 13\).
\begin{question}Use $h(x) = - x^{2} + 4 x - 1$ to evaluate:\newline
\begin{tabular}{|l|}\hline
$h(-4)$ \\ \hline
$h(- x)$ \\ \hline
$h(- t - 2)$ \\ \hline
\end{tabular}\newline
\soln{9cm}{Evaluating the function at $x = -4$ gives $f(-4) = - (-4)^{2} + 4 (-4) - 1 = -33$.\newline
Evaluating the function at $x = - x$ gives $f(- x) = - (- x)^{2} + 4 (- x) - 1 = - x^{2} - 4 x - 1$.\newline
Evaluating the function at $x = - t - 2$ gives $f(- t - 2) = - (- t - 2)^{2} + 4 (- t - 2) - 1 = - t^{2} - 8 t - 13$.\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) = - x^{2} + 4 x - 1 " src="/equation_images/%20%5Cdisplaystyle%20h%28x%29%20%3D%20-%20x%5E%7B2%7D%20%2B%204%20x%20-%201%20" alt="LaTeX: \displaystyle h(x) = - x^{2} + 4 x - 1 " data-equation-content=" \displaystyle h(x) = - x^{2} + 4 x - 1 " /> 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%20-4%20" alt="LaTeX: \displaystyle x = -4 " data-equation-content=" \displaystyle x = -4 " /> gives <img class="equation_image" title=" \displaystyle f(-4) = - (-4)^{2} + 4 (-4) - 1 = -33 " src="/equation_images/%20%5Cdisplaystyle%20f%28-4%29%20%3D%20-%20%28-4%29%5E%7B2%7D%20%2B%204%20%28-4%29%20-%201%20%3D%20-33%20" alt="LaTeX: \displaystyle f(-4) = - (-4)^{2} + 4 (-4) - 1 = -33 " data-equation-content=" \displaystyle f(-4) = - (-4)^{2} + 4 (-4) - 1 = -33 " /> .<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) = - (- x)^{2} + 4 (- x) - 1 = - x^{2} - 4 x - 1 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%20x%29%20%3D%20-%20%28-%20x%29%5E%7B2%7D%20%2B%204%20%28-%20x%29%20-%201%20%3D%20-%20x%5E%7B2%7D%20-%204%20x%20-%201%20" alt="LaTeX: \displaystyle f(- x) = - (- x)^{2} + 4 (- x) - 1 = - x^{2} - 4 x - 1 " data-equation-content=" \displaystyle f(- x) = - (- x)^{2} + 4 (- x) - 1 = - x^{2} - 4 x - 1 " /> .<br>
Evaluating the function at <img class="equation_image" title=" \displaystyle x = - t - 2 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-%20t%20-%202%20" alt="LaTeX: \displaystyle x = - t - 2 " data-equation-content=" \displaystyle x = - t - 2 " /> gives <img class="equation_image" title=" \displaystyle f(- t - 2) = - (- t - 2)^{2} + 4 (- t - 2) - 1 = - t^{2} - 8 t - 13 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%20t%20-%202%29%20%3D%20-%20%28-%20t%20-%202%29%5E%7B2%7D%20%2B%204%20%28-%20t%20-%202%29%20-%201%20%3D%20-%20t%5E%7B2%7D%20-%208%20t%20-%2013%20" alt="LaTeX: \displaystyle f(- t - 2) = - (- t - 2)^{2} + 4 (- t - 2) - 1 = - t^{2} - 8 t - 13 " data-equation-content=" \displaystyle f(- t - 2) = - (- t - 2)^{2} + 4 (- t - 2) - 1 = - t^{2} - 8 t - 13 " /> .<br>
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