document.write( "Question 744398: hello! i need help getting the vertex form of y=-3x^2+12x-8. I have a test tommarow and i dont get it:( \n" ); document.write( "

Algebra.Com's Answer #453323 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
The vertex form of the equation of a parabola is
\n" ); document.write( " $\"y=a%28x-h%29%5E2%2Bk\"$ with a coefficient $\"a\"$ and using the coordinates (h,k) of the vertex.
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\n" ); document.write( "A SLOW AND EASY WAY:
\n" ); document.write( "If you expand the square in $\"y=a%28x-h%29%5E2%2Bk\"$ you get
\n" ); document.write( " $\"y=a%28x%5E2-2hx%2Bh%5E2%29%2Bk\"$ --> $\"y=a%5Ex%5E2-2ahx%2Bah%5E2%2Bk\"$
\n" ); document.write( "If you compare that to $\"y=-3x%5E2%2B12x-8\"$ you realize that:
\n" ); document.write( "the coefficient of $\"x%5E2\"$ is $\"a=-3\"$ , and
\n" ); document.write( "the coefficient of $\"x\"$ is $\"-2ah=12\"$
\n" ); document.write( "That gives you the values of $\"a\"$ and $\"h\"$ :
\n" ); document.write( " $\"a=-3\"$ was clear, and substituting that value in $\"-2ah=12\"$ you get
\n" ); document.write( " $\"-2%2A%28-3%29%2Ah=12\"$ --> $\"6h=12\"$ --> $\"h=12%2F6\"$ --> $\"h=2\"$
\n" ); document.write( "Plugging those values into
\n" ); document.write( " $\"y=a%28x-h%29%5E2%2Bk\"$ you get
\n" ); document.write( " $\"y=-3%28x-2%29%5E2%2Bk\"$ --> $\"y=-3%28x-2%29%5E2%2Bk\"$ --> $\"y=-3%28x%5E2-4x%2B4%29%2Bk\"$ --> $\"y=-3x%5E2%2B12x-12%2Bk\"$
\n" ); document.write( "Comparing that last equation to $\"y=-3x%5E2%2B12x-8\"$ , you realize that the independent term (the part without any $\"x\"$ ) is
\n" ); document.write( " $\"-12%2Bk=-8\"$ --> $\"k=-8%2B12\"$ --> $\"k=4\"$
\n" ); document.write( "Plugging the values found for $\"a\"$ , $\"h\"$ , and $\"k\"$ into $\"y=a%28x-h%29%5E2%2Bk\"$ you get
\n" ); document.write( " $\"highlight%28y=-3%28x-2%29%5E2%2B4%29\"$ .
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\n" ); document.write( "THE FAST AND STEEP WAY that makes you look so smart:
\n" ); document.write( " $\"y=-3x%5E2%2B12x-8\"$ --> $\"y=-3%28x%5E2-4x%29-8\"$ (taking out (-3) as common factor from $\"-3x%5E2%2B12x\"$
\n" ); document.write( " $\"y=-3%28x%5E2-4x%29-8\"$ --> $\"y=-3%28x%5E2-4x%2B4%29%2B3%2A4-8\"$ (adding $\"3%2A4\"$ and $\"-3%284%29\"$ which cancel out)
\n" ); document.write( " $\"y=-3%28x%5E2-4x%2B4%29%2B3%2A4-8\"$ --> $\"y=-3%28x%5E2-4x%2B4%29%2B12-8\"$ --> $\"y=-3%28x%5E2-4x%2B4%29%2B4\"$ --> $\"highlight%28y=-3%28x-2%29%5E2%2B4%29\"$ .
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\n" ); document.write( "THE MEMORIZED FORMULA WAY:
\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$ --> $\"y=a%28x%2Bb%2F2a%29%5E2%2B%284ac-b%5E2%29%2F4a\"$
\n" ); document.write( "For $\"y=-3x%5E2%2B12x-8\"$ , $\"a=-3\"$ , $\"b=12\"$ and $\"c=-8\"$ so
\n" ); document.write( " $\"b%2F2a=12%2F%282%2A%28-3%29%29=12%2F%28-6%29=-2\"$ and
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so
\n" ); document.write( "the vertex form is $\"highlight%28y=-3%28x-2%29%5E2%2B4%29\"$ .
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\n" ); document.write( "NOTE:
\n" ); document.write( "If your teacher favors the fast and steep way, show your teacher that way (even if you figured it out a different way on a separate piece of paper). \n" ); document.write( "

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