document.write( "Question 178080: Quadratic relations
\n" ); document.write( "7) Sketch a graph of each quadratic. Label the x-intercepts and the vertex.
\n" ); document.write( "b) y=2(x-3)(x+1) pleaseeeeeeeeeeee
\n" ); document.write( "thank you very muchhhhhhhhhhhh \n" ); document.write( "

Algebra.Com's Answer #133036 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"y+=+2%28x-3%29%28x%2B1%29\"$
\n" ); document.write( "The x-intercepts are the roots. The roots are values of $\"x\"$ that make
\n" ); document.write( " $\"Y=0\"$ . Looking at the equation, if $\"x=3\"$
\n" ); document.write( " $\"y+=+2%283-3%29%28x%2B1%29\"$
\n" ); document.write( " $\"0+=+2%2A0%2A%28x%2B1%29\"$
\n" ); document.write( "And if $\"x=-1\"$
\n" ); document.write( " $\"y+=+2%28x-3%29%28-1%2B1%29\"$
\n" ); document.write( " $\"0+=+2%28x-3%29%2A0\"$
\n" ); document.write( "So, $\"x=3\"$ and $\"x=-1\"$ must be the x-intercepts.
\n" ); document.write( "The vertex is always exactly midway between the roots, so
\n" ); document.write( " $\"x%5Bv%5D+=+%28-1+%2B+3%29%2F2\"$
\n" ); document.write( " $\"x%5Bv%5D+=+2%2F2\"$
\n" ); document.write( " $\"x%5Bv%5D+=+1\"$
\n" ); document.write( "So, the vertex is at ( $\"1\"$ , $\"y%5Bv%5D\"$ )
\n" ); document.write( " $\"y+=+2%28x-3%29%28x%2B1%29\"$
\n" ); document.write( " $\"y%5Bv%5D+=+2%281-3%29%281%2B1%29\"$
\n" ); document.write( " $\"y%5Bv%5D+=+2%2A%28-2%29%2A2\"$
\n" ); document.write( " $\"y%5Bv%5D+=+-8\"$
\n" ); document.write( "So, the vertex must be at (1,-8)
\n" ); document.write( "Now I'll graph the equation to prove what I said
\n" ); document.write( " $\"y+=+2%28x-3%29%28x%2B1%29\"$
\n" ); document.write( " $\"y+=+2%2A%28x%5E2+-+2x+-+3%29\"$
\n" ); document.write( " $\"y+=+2x%5E2+-+4x+-+6\"$
\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+2x%5E2+-+4x+-+6%29+\"$ \n" ); document.write( "

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