document.write( "Question 1010344: If there is only one solution to the equation 0= -x^2 + bx -8 what are the possible values of b? \n" ); document.write( "

Algebra.Com's Answer #625758 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+0+=+-x%5E2+%2B+b%2Ax+-+8+\"$
\n" ); document.write( "One solution means this parabola touches the
\n" ); document.write( "x-axis at one point
\n" ); document.write( "The quadratic formula is:
\n" ); document.write( " $\"+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "Just get rid of the part that gives 2 solutions,
\n" ); document.write( "the +- part.
\n" ); document.write( " $\"+x+=+%28-b+%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"+x+=+%28-b%29%2F%28-2%29+\"$
\n" ); document.write( " $\"+x+=+b%2F2+\"$
\n" ); document.write( "--------------
\n" ); document.write( " $\"+0+=+-%28b%2F2%29%5E2+%2B+b%2A%28b%2F2%29+-+8+\"$
\n" ); document.write( " $\"+0+=+-b%5E2%2F4+%2B+b%5E2%2F2+-+8+\"$
\n" ); document.write( " $\"+0+=+b%5E2%2F4+-+8+\"$
\n" ); document.write( " $\"+b%5E2%2F4+=+8+\"$
\n" ); document.write( " $\"+b%5E2+=+32+\"$
\n" ); document.write( " $\"+b+=+4%2Asqrt%282%29+\"$
\n" ); document.write( " $\"+b+=+-4%2Asqrt%282%29+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "check the answers:
\n" ); document.write( " $\"+sqrt%28+b%5E2-4%2Aa%2Ac+%29+\"$ must equal zero, so
\n" ); document.write( " $\"+b%5E2+=+4a%2Ac+\"$
\n" ); document.write( " $\"+%28+4%2Asqrt%282%29+%29%5E2+=+4%2A%28+-1+%29%2A%28-8%29+\"$
\n" ); document.write( " $\"+16%2A2+=+32+\"$
\n" ); document.write( " $\"+32+=+32+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+b%5E2+=+4a%2Ac+\"$
\n" ); document.write( " $\"+%28+-4%2Asqrt%282%29+%29%5E2+=+4%2A%28+-1+%29%2A%28-8%29+\"$
\n" ); document.write( " $\"+16%2A2+=+32+\"$
\n" ); document.write( " $\"+32+=+32+\"$
\n" ); document.write( "OK
\n" ); document.write( "Here is the plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-2%2C+10%2C+-10%2C+2%2C+-x%5E2+%2B+4%2Asqrt%282%29%2Ax+-+8+%29+\"$ \n" ); document.write( "

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