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Questions: Algebra BusinessCalculus
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Use \(\displaystyle h(x) = 8 x^{2} + 5 x - 3\) to evaluate:
Evaluating the function at \(\displaystyle x = 3\) gives \(\displaystyle f(3) = 8 (3)^{2} + 5 (3) - 3 = 84\).
Evaluating the function at \(\displaystyle x = - 2 x\) gives \(\displaystyle f(- 2 x) = 8 (- 2 x)^{2} + 5 (- 2 x) - 3 = 32 x^{2} - 10 x - 3\).
Evaluating the function at \(\displaystyle x = 3 - t\) gives \(\displaystyle f(3 - t) = 8 (3 - t)^{2} + 5 (3 - t) - 3 = 8 t^{2} - 53 t + 84\).
\begin{question}Use $h(x) = 8 x^{2} + 5 x - 3$ to evaluate:\newline
\begin{tabular}{|l|}\hline
$h(3)$ \\ \hline
$h(- 2 x)$ \\ \hline
$h(3 - t)$ \\ \hline
\end{tabular}\newline
\soln{9cm}{Evaluating the function at $x = 3$ gives $f(3) = 8 (3)^{2} + 5 (3) - 3 = 84$.\newline
Evaluating the function at $x = - 2 x$ gives $f(- 2 x) = 8 (- 2 x)^{2} + 5 (- 2 x) - 3 = 32 x^{2} - 10 x - 3$.\newline
Evaluating the function at $x = 3 - t$ gives $f(3 - t) = 8 (3 - t)^{2} + 5 (3 - t) - 3 = 8 t^{2} - 53 t + 84$.\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) = 8 x^{2} + 5 x - 3 " src="/equation_images/%20%5Cdisplaystyle%20h%28x%29%20%3D%208%20x%5E%7B2%7D%20%2B%205%20x%20-%203%20" alt="LaTeX: \displaystyle h(x) = 8 x^{2} + 5 x - 3 " data-equation-content=" \displaystyle h(x) = 8 x^{2} + 5 x - 3 " /> to evaluate:<br>
</p> </p><p> <p>Evaluating the function at <img class="equation_image" title=" \displaystyle x = 3 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%203%20" alt="LaTeX: \displaystyle x = 3 " data-equation-content=" \displaystyle x = 3 " /> gives <img class="equation_image" title=" \displaystyle f(3) = 8 (3)^{2} + 5 (3) - 3 = 84 " src="/equation_images/%20%5Cdisplaystyle%20f%283%29%20%3D%208%20%283%29%5E%7B2%7D%20%2B%205%20%283%29%20-%203%20%3D%2084%20" alt="LaTeX: \displaystyle f(3) = 8 (3)^{2} + 5 (3) - 3 = 84 " data-equation-content=" \displaystyle f(3) = 8 (3)^{2} + 5 (3) - 3 = 84 " /> .<br>
Evaluating the function at <img class="equation_image" title=" \displaystyle x = - 2 x " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-%202%20x%20" alt="LaTeX: \displaystyle x = - 2 x " data-equation-content=" \displaystyle x = - 2 x " /> gives <img class="equation_image" title=" \displaystyle f(- 2 x) = 8 (- 2 x)^{2} + 5 (- 2 x) - 3 = 32 x^{2} - 10 x - 3 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%202%20x%29%20%3D%208%20%28-%202%20x%29%5E%7B2%7D%20%2B%205%20%28-%202%20x%29%20-%203%20%3D%2032%20x%5E%7B2%7D%20-%2010%20x%20-%203%20" alt="LaTeX: \displaystyle f(- 2 x) = 8 (- 2 x)^{2} + 5 (- 2 x) - 3 = 32 x^{2} - 10 x - 3 " data-equation-content=" \displaystyle f(- 2 x) = 8 (- 2 x)^{2} + 5 (- 2 x) - 3 = 32 x^{2} - 10 x - 3 " /> .<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) = 8 (3 - t)^{2} + 5 (3 - t) - 3 = 8 t^{2} - 53 t + 84 " src="/equation_images/%20%5Cdisplaystyle%20f%283%20-%20t%29%20%3D%208%20%283%20-%20t%29%5E%7B2%7D%20%2B%205%20%283%20-%20t%29%20-%203%20%3D%208%20t%5E%7B2%7D%20-%2053%20t%20%2B%2084%20" alt="LaTeX: \displaystyle f(3 - t) = 8 (3 - t)^{2} + 5 (3 - t) - 3 = 8 t^{2} - 53 t + 84 " data-equation-content=" \displaystyle f(3 - t) = 8 (3 - t)^{2} + 5 (3 - t) - 3 = 8 t^{2} - 53 t + 84 " /> .<br>
</p> </p>