document.write( "Question 192356: if y=8x^2 + 4x-1 is expressed in the form y=a(x-h)^2+k, where a, h, and k are constants, what is the value of k ? \n" ); document.write( "

Algebra.Com's Answer #144402 by RAY100(1637) $\"\"$ $\"About$

You can put this solution on YOUR website!
y=8x^2+4x-1 to form y=a(x-h)^2+k\r
\n" ); document.write( "\n" ); document.write( "y=8(x^2+x/2)-1\r
\n" ); document.write( "\n" ); document.write( "now must complete square of bracket terms\r
\n" ); document.write( "\n" ); document.write( "y=8(x^2 +x/2 +1/16) -1 -8(1/16)
\n" ); document.write( "simplify
\n" ); document.write( "y=8(x+1/4)^2-1.5\r
\n" ); document.write( "\n" ); document.write( "this fits form with \r
\n" ); document.write( "\n" ); document.write( "a=(8)
\n" ); document.write( "h=(-1/4)
\n" ); document.write( "k=(-1.5)\r
\n" ); document.write( "\n" ); document.write( "checking
\n" ); document.write( "let x=3 solve for y
\n" ); document.write( "initial eqn y=8x^2+4x-1= 8(3^2) +4(3)-1=72+12-1=83
\n" ); document.write( "final form y=8(x+1/4)^2-1.5=8(3.25)^2-1.5= 8(10.5625)-1.5=84.5-1.5=83 ok\r
\n" ); document.write( "\n" ); document.write( "to complete the square we take coefficient of middle term, divide by two, and square it
\n" ); document.write( "ie (1/2) , (1/2)/2=1/4, (1/4)^2=(1/16)
\n" ); document.write( "this becomes constant term of \"square\"
\n" ); document.write( "since we added this to complete square terms we must subst from constant term to balance eqn. In this case we added 8(1/16) in total therefore we substract (8/16) from constant \n" ); document.write( "

\n" );