document.write( "Question 1052785: Workout the gradient and turning point p (x, y) of the curve y=ax^2+bx+c.use the turning point p (x, y) to find the turning point of the curve y=-2x^2-2x+3 \n" ); document.write( "

Algebra.Com's Answer #668135 by Fombitz(32388) $\"\"$ $\"About$

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Covert the equation to vertex form,
\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$
\n" ); document.write( " $\"y=a%28x%5E2%2B%28b%2Fa%29x%29%2Bc\"$
\n" ); document.write( " $\"y=a%28x%5E2%2B%28b%2Fa%29x%2B%28b%2F%282a%29%29%5E2%29%2Bc-a%28b%2F%282a%29%29%5E2\"$
\n" ); document.write( " $\"y=a%28x%2B%28b%2F%282a%29%29%29%5E2%2B%28c-b%5E2%2F%284a%29%29\"$
\n" ); document.write( "So then the vertex(turning point) is
\n" ); document.write( "( $\"-b%2F%282a%29\"$ , $\"c-b%5E2%2F%284a%29\"$ )
\n" ); document.write( "So then for the example,
\n" ); document.write( " $\"a=-2\"$
\n" ); document.write( " $\"b=-2\"$
\n" ); document.write( " $\"c=3\"$
\n" ); document.write( "The turning point would be,
\n" ); document.write( "( $\"-%28-2%2F%282%28-2%29%29%29\"$ , $\"3-%28-2%29%5E2%2F%284%28-2%29%29\"$ )
\n" ); document.write( "( $\"-1%2F2\"$ , $\"7%2F2\"$ ) \n" ); document.write( "

\n" );