\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Use \(\displaystyle h(x) = 4 x^{2} - 6 x + 5\) to evaluate:
Evaluating the function at \(\displaystyle x = 7\) gives \(\displaystyle f(7) = 4 (7)^{2} - 6 (7) + 5 = 159\).
Evaluating the function at \(\displaystyle x = - 3 x\) gives \(\displaystyle f(- 3 x) = 4 (- 3 x)^{2} - 6 (- 3 x) + 5 = 36 x^{2} + 18 x + 5\).
Evaluating the function at \(\displaystyle x = - t - 2\) gives \(\displaystyle f(- t - 2) = 4 (- t - 2)^{2} - 6 (- t - 2) + 5 = 4 t^{2} + 22 t + 33\).
\begin{question}Use $h(x) = 4 x^{2} - 6 x + 5$ to evaluate:\newline
\begin{tabular}{|l|}\hline
$h(7)$ \\ \hline
$h(- 3 x)$ \\ \hline
$h(- t - 2)$ \\ \hline
\end{tabular}\newline
\soln{9cm}{Evaluating the function at $x = 7$ gives $f(7) = 4 (7)^{2} - 6 (7) + 5 = 159$.\newline
Evaluating the function at $x = - 3 x$ gives $f(- 3 x) = 4 (- 3 x)^{2} - 6 (- 3 x) + 5 = 36 x^{2} + 18 x + 5$.\newline
Evaluating the function at $x = - t - 2$ gives $f(- t - 2) = 4 (- t - 2)^{2} - 6 (- t - 2) + 5 = 4 t^{2} + 22 t + 33$.\newline
}
\end{question}
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}
\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}
\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}
\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue
\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) = 4 x^{2} - 6 x + 5 " src="/equation_images/%20%5Cdisplaystyle%20h%28x%29%20%3D%204%20x%5E%7B2%7D%20-%206%20x%20%2B%205%20" alt="LaTeX: \displaystyle h(x) = 4 x^{2} - 6 x + 5 " data-equation-content=" \displaystyle h(x) = 4 x^{2} - 6 x + 5 " /> to evaluate:<br>
</p> </p><p> <p>Evaluating the function at <img class="equation_image" title=" \displaystyle x = 7 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%207%20" alt="LaTeX: \displaystyle x = 7 " data-equation-content=" \displaystyle x = 7 " /> gives <img class="equation_image" title=" \displaystyle f(7) = 4 (7)^{2} - 6 (7) + 5 = 159 " src="/equation_images/%20%5Cdisplaystyle%20f%287%29%20%3D%204%20%287%29%5E%7B2%7D%20-%206%20%287%29%20%2B%205%20%3D%20159%20" alt="LaTeX: \displaystyle f(7) = 4 (7)^{2} - 6 (7) + 5 = 159 " data-equation-content=" \displaystyle f(7) = 4 (7)^{2} - 6 (7) + 5 = 159 " /> .<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) = 4 (- 3 x)^{2} - 6 (- 3 x) + 5 = 36 x^{2} + 18 x + 5 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%203%20x%29%20%3D%204%20%28-%203%20x%29%5E%7B2%7D%20-%206%20%28-%203%20x%29%20%2B%205%20%3D%2036%20x%5E%7B2%7D%20%2B%2018%20x%20%2B%205%20" alt="LaTeX: \displaystyle f(- 3 x) = 4 (- 3 x)^{2} - 6 (- 3 x) + 5 = 36 x^{2} + 18 x + 5 " data-equation-content=" \displaystyle f(- 3 x) = 4 (- 3 x)^{2} - 6 (- 3 x) + 5 = 36 x^{2} + 18 x + 5 " /> .<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) = 4 (- t - 2)^{2} - 6 (- t - 2) + 5 = 4 t^{2} + 22 t + 33 " src="/equation_images/%20%5Cdisplaystyle%20f%28-%20t%20-%202%29%20%3D%204%20%28-%20t%20-%202%29%5E%7B2%7D%20-%206%20%28-%20t%20-%202%29%20%2B%205%20%3D%204%20t%5E%7B2%7D%20%2B%2022%20t%20%2B%2033%20" alt="LaTeX: \displaystyle f(- t - 2) = 4 (- t - 2)^{2} - 6 (- t - 2) + 5 = 4 t^{2} + 22 t + 33 " data-equation-content=" \displaystyle f(- t - 2) = 4 (- t - 2)^{2} - 6 (- t - 2) + 5 = 4 t^{2} + 22 t + 33 " /> .<br>
</p> </p>