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Questions: Algebra BusinessCalculus
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Write the function \(\displaystyle f(x)=x^{2} + 6 x\) in vertex form and identify the vertex.
\(\displaystyle h = -\frac{b}{2a}\) and \(\displaystyle k=f(h)\). Using each formula gives \(\displaystyle h= -3\) and \(\displaystyle k = -9\). The vertex is located at \(\displaystyle (-3,-9)\) and the vertex form is \(\displaystyle f(x) = a(x-h)^2+k=\left(x + 3\right)^{2} - 9\).
\begin{question}Write the function $f(x)=x^{2} + 6 x$ in vertex form and identify the vertex.
\soln{9cm}{$h = -\frac{b}{2a}$ and $k=f(h)$. Using each formula gives $h= -3$ and $k = -9$. The vertex is located at $(-3,-9)$ and the vertex form is $f(x) = a(x-h)^2+k=\left(x + 3\right)^{2} - 9$. }
\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>Write the function <img class="equation_image" title=" \displaystyle f(x)=x^{2} + 6 x " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%3Dx%5E%7B2%7D%20%2B%206%20x%20" alt="LaTeX: \displaystyle f(x)=x^{2} + 6 x " data-equation-content=" \displaystyle f(x)=x^{2} + 6 x " /> in vertex form and identify the vertex. </p> </p><p> <p> <img class="equation_image" title=" \displaystyle h = -\frac{b}{2a} " src="/equation_images/%20%5Cdisplaystyle%20h%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D%20" alt="LaTeX: \displaystyle h = -\frac{b}{2a} " data-equation-content=" \displaystyle h = -\frac{b}{2a} " /> and <img class="equation_image" title=" \displaystyle k=f(h) " src="/equation_images/%20%5Cdisplaystyle%20k%3Df%28h%29%20" alt="LaTeX: \displaystyle k=f(h) " data-equation-content=" \displaystyle k=f(h) " /> . Using each formula gives <img class="equation_image" title=" \displaystyle h= -3 " src="/equation_images/%20%5Cdisplaystyle%20h%3D%20-3%20" alt="LaTeX: \displaystyle h= -3 " data-equation-content=" \displaystyle h= -3 " /> and <img class="equation_image" title=" \displaystyle k = -9 " src="/equation_images/%20%5Cdisplaystyle%20k%20%3D%20-9%20" alt="LaTeX: \displaystyle k = -9 " data-equation-content=" \displaystyle k = -9 " /> . The vertex is located at <img class="equation_image" title=" \displaystyle (-3,-9) " src="/equation_images/%20%5Cdisplaystyle%20%28-3%2C-9%29%20" alt="LaTeX: \displaystyle (-3,-9) " data-equation-content=" \displaystyle (-3,-9) " /> and the vertex form is <img class="equation_image" title=" \displaystyle f(x) = a(x-h)^2+k=\left(x + 3\right)^{2} - 9 " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20a%28x-h%29%5E2%2Bk%3D%5Cleft%28x%20%2B%203%5Cright%29%5E%7B2%7D%20-%209%20" alt="LaTeX: \displaystyle f(x) = a(x-h)^2+k=\left(x + 3\right)^{2} - 9 " data-equation-content=" \displaystyle f(x) = a(x-h)^2+k=\left(x + 3\right)^{2} - 9 " /> . </p> </p>