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Questions: Algebra BusinessCalculus
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Find the domain and range of \(\displaystyle f(x)=4 x^{2} - 16 x + 18 \)
The domain of every polynomial is all real numbers. The sign of \(\displaystyle a\) is positive so the function has a minimum value at the vertex. The vertex is located at \(\displaystyle h=\frac{-b}{2a}=2\) and \(\displaystyle k=f(h)=2\). This gives the range as \(\displaystyle [2,\infty)\)
\begin{question}Find the domain and range of $f(x)=4 x^{2} - 16 x + 18 $
\soln{9cm}{The domain of every polynomial is all real numbers. The sign of $a$ is positive so the function has a minimum value at the vertex. The vertex is located at $h=\frac{-b}{2a}=2$ and $k=f(h)=2$. This gives the range as $[2,\infty)$}
\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)=4 x^{2} - 16 x + 18 " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%3D4%20x%5E%7B2%7D%20-%2016%20x%20%2B%2018%20%20" alt="LaTeX: \displaystyle f(x)=4 x^{2} - 16 x + 18 " data-equation-content=" \displaystyle f(x)=4 x^{2} - 16 x + 18 " /> </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 positive so the function has a minimum value at the vertex. The vertex is located at <img class="equation_image" title=" \displaystyle h=\frac{-b}{2a}=2 " src="/equation_images/%20%5Cdisplaystyle%20h%3D%5Cfrac%7B-b%7D%7B2a%7D%3D2%20" alt="LaTeX: \displaystyle h=\frac{-b}{2a}=2 " data-equation-content=" \displaystyle h=\frac{-b}{2a}=2 " /> and <img class="equation_image" title=" \displaystyle k=f(h)=2 " src="/equation_images/%20%5Cdisplaystyle%20k%3Df%28h%29%3D2%20" alt="LaTeX: \displaystyle k=f(h)=2 " data-equation-content=" \displaystyle k=f(h)=2 " /> . This gives the range as <img class="equation_image" title=" \displaystyle [2,\infty) " src="/equation_images/%20%5Cdisplaystyle%20%5B2%2C%5Cinfty%29%20" alt="LaTeX: \displaystyle [2,\infty) " data-equation-content=" \displaystyle [2,\infty) " /> </p> </p>