document.write( "Question 1092312: Find the y-intercept of the line with gradient -3 that is tangential to the parabola
\n" ); document.write( "y = 2x^2-5x + 1. \n" ); document.write( "

Algebra.Com's Answer #706909 by josmiceli(19441) $\"\"$ $\"About$

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Find the derivative y'
\n" ); document.write( " $\"+y%5B1%5D+=+4x+-+5+\"$
\n" ); document.write( "You are given y' = -3
\n" ); document.write( " $\"+4x+-+5+=+-3+\"$
\n" ); document.write( " $\"+4x+=+2+\"$
\n" ); document.write( " $\"+x+=+1%2F2+\"$
\n" ); document.write( "Now find $\"+y+\"$ on the parabola
\n" ); document.write( "where slope = $\"+-3+\"$
\n" ); document.write( " $\"+y+=+2%2A%281%2F2%29%5E2+-+5%2A%281%2F2%29+%2B+1+\"$
\n" ); document.write( " $\"+y+=+1%2F2+-+5%2F2+%2B+2%2F2+\"$
\n" ); document.write( " $\"+y+=+-1+\"$
\n" ); document.write( "------------------
\n" ); document.write( "The line is tangent to the parabola at the point ( 1/2, -1 )
\n" ); document.write( "The slope intercept form is:
\n" ); document.write( " $\"+y+=+m%2Ax+%2B+b+\"$
\n" ); document.write( "where $\"+b+\"$ is the y-intercept
\n" ); document.write( " $\"+-1+=+%28-3%29%2A%281%2F2%29+%2B+b+\"$
\n" ); document.write( " $\"+-1+=+-3%2F2+%2B+b+\"$
\n" ); document.write( " $\"+b+=+1%2F2+\"$
\n" ); document.write( "The y-intercept is at ( 0, 1/2 )
\n" ); document.write( "------------------------------
\n" ); document.write( "Check:
\n" ); document.write( "Here's the plot of parabola and straight line:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-6%2C+6%2C+-6%2C+6%2C+2x%5E2+-+5x+%2B+1%2C+-3x+%2B+1%2F2+%29+\"$
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