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Use \(\displaystyle h(x) = - 3 x^{2} + 9 x - 8\) to evaluate:

Evaluating the function at \(\displaystyle x = -7\) gives \(\displaystyle f(-7) = - 3 (-7)^{2} + 9 (-7) - 8 = -218\).
Evaluating the function at \(\displaystyle x = - x\) gives \(\displaystyle f(- x) = - 3 (- x)^{2} + 9 (- x) - 8 = - 3 x^{2} - 9 x - 8\).
Evaluating the function at \(\displaystyle x = - t - 3\) gives \(\displaystyle f(- t - 3) = - 3 (- t - 3)^{2} + 9 (- t - 3) - 8 = - 3 t^{2} - 27 t - 62\).

Download \(\LaTeX\) 

\begin{question}Use $h(x) = - 3 x^{2} + 9 x - 8$ to evaluate:\newline
\begin{tabular}{|l|}\hline
$h(-7)$ \\ \hline
$h(- x)$ \\ \hline
$h(- t - 3)$ \\ \hline
\end{tabular}\newline

    \soln{9cm}{Evaluating the function at $x = -7$ gives $f(-7) = - 3 (-7)^{2} + 9 (-7) - 8 = -218$.\newline
 Evaluating the function at $x = - x$ gives $f(- x) = - 3 (- x)^{2} + 9 (- x) - 8 = - 3 x^{2} - 9 x - 8$.\newline
 Evaluating the function at $x = - t - 3$ gives $f(- t - 3) = - 3 (- t - 3)^{2} + 9 (- t - 3) - 8 = - 3 t^{2} - 27 t - 62$.\newline
 }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

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HTML for Canvas 
<p> <p>Use  <img class="equation_image" title=" \displaystyle h(x) = - 3 x^{2} + 9 x - 8 " src="/equation_images/%20%5Cdisplaystyle%20h%28x%29%20%3D%20-%203%20x%5E%7B2%7D%20%2B%209%20x%20-%208%20" alt="LaTeX:  \displaystyle h(x) = - 3 x^{2} + 9 x - 8 " data-equation-content=" \displaystyle h(x) = - 3 x^{2} + 9 x - 8 " />  to evaluate:<br>
</p> </p>
HTML for Canvas
<p> <p>Evaluating the function at  <img class="equation_image" title=" \displaystyle x = -7 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-7%20" alt="LaTeX:  \displaystyle x = -7 " data-equation-content=" \displaystyle x = -7 " />  gives  <img class="equation_image" title=" \displaystyle f(-7) = - 3 (-7)^{2} + 9 (-7) - 8 = -218 " src="/equation_images/%20%5Cdisplaystyle%20f%28-7%29%20%3D%20-%203%20%28-7%29%5E%7B2%7D%20%2B%209%20%28-7%29%20-%208%20%3D%20-218%20" alt="LaTeX:  \displaystyle f(-7) = - 3 (-7)^{2} + 9 (-7) - 8 = -218 " data-equation-content=" \displaystyle f(-7) = - 3 (-7)^{2} + 9 (-7) - 8 = -218 " /> .<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) = - 3 (- x)^{2} + 9 (- x) - 8 = - 3 x^{2} - 9 x - 8 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%20x%29%20%3D%20-%203%20%28-%20x%29%5E%7B2%7D%20%2B%209%20%28-%20x%29%20-%208%20%3D%20-%203%20x%5E%7B2%7D%20-%209%20x%20-%208%20" alt="LaTeX:  \displaystyle f(- x) = - 3 (- x)^{2} + 9 (- x) - 8 = - 3 x^{2} - 9 x - 8 " data-equation-content=" \displaystyle f(- x) = - 3 (- x)^{2} + 9 (- x) - 8 = - 3 x^{2} - 9 x - 8 " /> .<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) = - 3 (- t - 3)^{2} + 9 (- t - 3) - 8 = - 3 t^{2} - 27 t - 62 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%20t%20-%203%29%20%3D%20-%203%20%28-%20t%20-%203%29%5E%7B2%7D%20%2B%209%20%28-%20t%20-%203%29%20-%208%20%3D%20-%203%20t%5E%7B2%7D%20-%2027%20t%20-%2062%20" alt="LaTeX:  \displaystyle f(- t - 3) = - 3 (- t - 3)^{2} + 9 (- t - 3) - 8 = - 3 t^{2} - 27 t - 62 " data-equation-content=" \displaystyle f(- t - 3) = - 3 (- t - 3)^{2} + 9 (- t - 3) - 8 = - 3 t^{2} - 27 t - 62 " /> .<br>
 </p> </p>