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Questions: Algebra BusinessCalculus
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Find the domain and range of \(\displaystyle f(x)=- 2 x^{2} - 28 x - 103 \)
The domain of every polynomial is all real numbers. The sign of \(\displaystyle a\) is negative so the function has a maximum value at the vertex. The vertex is located at \(\displaystyle h=\frac{-b}{2a}=-7\) and \(\displaystyle k=f(h)=-5\). This gives the range as \(\displaystyle (-\infty,-5]\)
\begin{question}Find the domain and range of $f(x)=- 2 x^{2} - 28 x - 103 $
\soln{9cm}{The domain of every polynomial is all real numbers. The sign of $a$ is negative so the function has a maximum value at the vertex. The vertex is located at $h=\frac{-b}{2a}=-7$ and $k=f(h)=-5$. This gives the range as $(-\infty,-5]$}
\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>Find the domain and range of <img class="equation_image" title=" \displaystyle f(x)=- 2 x^{2} - 28 x - 103 " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%3D-%202%20x%5E%7B2%7D%20-%2028%20x%20-%20103%20%20" alt="LaTeX: \displaystyle f(x)=- 2 x^{2} - 28 x - 103 " data-equation-content=" \displaystyle f(x)=- 2 x^{2} - 28 x - 103 " /> </p> </p><p> <p>The domain of every polynomial is all real numbers. The sign of <img class="equation_image" title=" \displaystyle a " src="/equation_images/%20%5Cdisplaystyle%20a%20" alt="LaTeX: \displaystyle a " data-equation-content=" \displaystyle a " /> is negative so the function has a maximum value at the vertex. The vertex is located at <img class="equation_image" title=" \displaystyle h=\frac{-b}{2a}=-7 " src="/equation_images/%20%5Cdisplaystyle%20h%3D%5Cfrac%7B-b%7D%7B2a%7D%3D-7%20" alt="LaTeX: \displaystyle h=\frac{-b}{2a}=-7 " data-equation-content=" \displaystyle h=\frac{-b}{2a}=-7 " /> and <img class="equation_image" title=" \displaystyle k=f(h)=-5 " src="/equation_images/%20%5Cdisplaystyle%20k%3Df%28h%29%3D-5%20" alt="LaTeX: \displaystyle k=f(h)=-5 " data-equation-content=" \displaystyle k=f(h)=-5 " /> . This gives the range as <img class="equation_image" title=" \displaystyle (-\infty,-5] " src="/equation_images/%20%5Cdisplaystyle%20%28-%5Cinfty%2C-5%5D%20" alt="LaTeX: \displaystyle (-\infty,-5] " data-equation-content=" \displaystyle (-\infty,-5] " /> </p> </p>