document.write( "Question 889068: Find $\"a\"$ such that $\"f%28x%29=ax%5E2%2B5x%2B6\"$ has a minimum value of $\"169%2F24\"$ \n" ); document.write( "

Algebra.Com's Answer #537873 by josgarithmetic(39631) $\"\"$ $\"About$

You can put this solution on YOUR website!
Complete the Square:
\n" ); document.write( " $\"f%28x%29=a%28x%5E2%2B%285%2F%28a2%29%29x%2B6%2Fa%29\"$
\n" ); document.write( " $\"a%28x%5E2%2B%285%2F%282a%29%29x%2B%285%2F%284a%29%29%5E2-%285%2F%284a%29%29%5E2%2B6%2Fa%29\"$
\n" ); document.write( " $\"a%28%28x%2B%285%2F%284a%29%29%29%5E2-%285%2F%284a%29%29%5E2%2B6%2Fa%29\"$
\n" ); document.write( " $\"a%28x%2B%285%2F%284a%29%29%29%5E2-a%285%2F%284a%29%29%5E2%2B6\"$ , almost finished standard form.\r
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\n" ); document.write( "\n" ); document.write( "The extreme value happens when $\"x=-%285%2F%284a%29%29\"$ and $\"y=highlight_green%28-a%285%2F%284a%29%29%5E2%2B6=169%2F24%29\"$ ; there you can solve for a.\r
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\n" ); document.write( "\n" ); document.write( " $\"-a%2A%2825%2F%2816a%5E2%29%29%2B6=169%2F24\"$
\n" ); document.write( " $\"-25%2F%2816a%29%2B6=169%2F24\"$
\n" ); document.write( " $\"6-25%2F%2816a%29=169%2F24\"$ , LCD is 16*3a.
\n" ); document.write( " $\"6%2A16%2A3a-25%2A16%2A3a%2F%2816a%29=169%2A16%2A3a%2F24\"$
\n" ); document.write( " $\"6%2A16%2A3a-75=169%2A2%2A3a\"$
\n" ); document.write( " $\"169%2A6a-18%2A16a=-75\"$
\n" ); document.write( " $\"726a=-75\"$
\n" ); document.write( " $\"a=-75%2F726\"$
\n" ); document.write( " $\"a=-3%2A25%2F%28242%2A3%29\"$
\n" ); document.write( " $\"highlight%28a=-25%2F242%29\"$ . \n" ); document.write( "

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