document.write( "Question 1089066: Find the largest value of c such that -2 is in the range of f(x)=x^2+3x+c. \n" ); document.write( "

Algebra.Com's Answer #703403 by Fombitz(32388) $\"\"$ $\"About$

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At the point that $\"-2\"$ is the minimum value, it is the y coordinate of the vertex.
\n" ); document.write( "So then complete the square to get into vertex form.
\n" ); document.write( " $\"x%5E2%2B3x%2Bc=-2\"$
\n" ); document.write( " $\"x%5E2%2B3x%2B%283%2F2%29%5E2%2Bc=-2%2B%283%2F2%29%5E2\"$
\n" ); document.write( " $\"%28x%2B3%2F2%29%5E2=-2-c%2B9%2F4\"$
\n" ); document.write( " $\"%28x%2B3%2F2%29%5E2=1%2F4-c\"$
\n" ); document.write( "At the vertex $\"x=-3%2F2\"$ so,
\n" ); document.write( " $\"1%2F4-c=0\"$
\n" ); document.write( " $\"c=1%2F4\"$ \r
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