document.write( "Question 942469: Find the coordinates of the vertex of the parabola y=x2-4x+1 by making use of the fact that at the vertex, the slope of the tangent line is zero. \n" ); document.write( "

Algebra.Com's Answer #574556 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
It's easier to just complete the square but ...
\n" ); document.write( "The slope of the tangent is also the value of the derivative.
\n" ); document.write( " $\"y=x%5E2-4x%2B1\"$
\n" ); document.write( " $\"dy%2Fdx=2x-4\"$
\n" ); document.write( "Set this equal to zero.
\n" ); document.write( " $\"2x-4=0\"$
\n" ); document.write( " $\"2x=4\"$
\n" ); document.write( " $\"x=2\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"y=a%28x-2%29%5E2%2Bb\"$
\n" ); document.write( " $\"y=a%28x%5E2-4x%2B4%29%2Bb\"$
\n" ); document.write( " $\"y=ax%5E2-4ax%2B4a%2Bb\"$
\n" ); document.write( "Comparing to the original equation,
\n" ); document.write( " $\"-4a=-4\"$
\n" ); document.write( " $\"a=1\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"4a%2Bb=1\"$
\n" ); document.write( " $\"4%2Bb=1\"$
\n" ); document.write( " $\"b=-3\"$
\n" ); document.write( "So the equation in vertex form is,
\n" ); document.write( " $\"y=%28x-2%29%5E2-3\"$
\n" ); document.write( "and the vertex is (2,-3)
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E2-4x%2B1%29\"$
\n" ); document.write( " \n" ); document.write( "

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