document.write( "Question 881498: g(x)=3x^2+12x+9
\n" ); document.write( "does this function have a minimum or maximum value
\n" ); document.write( "what is the function minimum or maximum value
\n" ); document.write( "where does the minimum or maximum value occur
\n" ); document.write( "x= \n" ); document.write( "

Algebra.Com's Answer #532263 by josgarithmetic(39617) $\"\"$ $\"About$

You can put this solution on YOUR website!
Have Min? YES because $\"3%3E0\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Use Completing the Square to put the function into standard form and read the vertex (the minimum point) from the equation. This shows how to Complete the Square.\r
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\n" ); document.write( "\n" ); document.write( "The function which you have is factorable enough that you can find the roots, and from the roots, find the x value at the vertex, and use this x value (exact mid point of the two roots) to compute the y value for the vertex.\r
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\n" ); document.write( "\n" ); document.write( " $\"g%28x%29=3%28x%2B1%29%28x%2B3%29\"$ , and finding roots:
\n" ); document.write( " $\"%28x%2B1%29%28x%2B3%29=0\"$
\n" ); document.write( " $\"x=-1\"$ or $\"x=-3\"$ .
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\n" ); document.write( "The exact middle of those x-intercepts is -2. This is the line of symmetry of the function and the minimum point of the parabola.
\n" ); document.write( " $\"g%28-2%29=3%28-2%2B1%29%28-2%2B3%29\"$
\n" ); document.write( " $\"3%28-1%29%281%29\"$
\n" ); document.write( " $\"highlight%28g%28-2%29=-3%29\"$ , the minimum value, vertex (-2,-3). \n" ); document.write( "

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