document.write( "Question 1194988: 1. Y=2x^2-5 2. Y=-3(x+1)^2+2. 3. y=1/2(x-2)^2-4 For each of these three separate quadratic equation find the
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Algebra.Com's Answer #827298 by MathLover1(20849) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "1. $\"y=2x%5E2-5+\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%5E2-5%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Domain: $\"R\"$ (all real numbers)\r
\n" ); document.write( "\n" ); document.write( "Range:{ $\"y\"$ element $\"R+\"$ : $\"y%3E=-5\"$ }\r
\n" ); document.write( "\n" ); document.write( "Direction of opening: opening $\"+up\"$ \r
\n" ); document.write( "\n" ); document.write( "Vertex: ( $\"0\"$ , $\"-5\"$ )\r
\n" ); document.write( "\n" ); document.write( "X-intercept: \r
\n" ); document.write( "\n" ); document.write( "set $\"y=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0=2x%5E2-5+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2x%5E2=5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2=5%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=sqrt%285%2F2%29\"$ or $\"x=-sqrt%285%2F2%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "so, X-intercept are at ( $\"sqrt%285%2F2%29\"$ , $\"0\"$ ) and ( $\"-sqrt%285%2F2%29\"$ , $\"0\"$ )\r
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\n" ); document.write( "\n" ); document.write( "Y-intercept: set $\"x=0\"$ => $\"y=-5+\"$ \r
\n" ); document.write( "\n" ); document.write( "and Y-intercept is at ( $\"0\"$ , $\"-5\"$ )\r
\n" ); document.write( "\n" ); document.write( "Axis of symmetry: $\"x=0\"$ \r
\n" ); document.write( "\n" ); document.write( "Expansion/compression: a stretch by a factor of $\"2\"$ in y-direction\r
\n" ); document.write( "\n" ); document.write( "Congruent to: $\"y=2%28x%5E2-5%2F2%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "MIN/MAX value: minimum at ( $\"0\"$ , $\"-5\"$ )\r
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\n" ); document.write( "\n" ); document.write( "2. $\"y=-3%28x%2B1%29%5E2%2B2\"$
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3%28x%2B1%29%5E2%2B2%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Domain: $\"R\"$ (all real numbers)\r
\n" ); document.write( "\n" ); document.write( "Range: { $\"y\"$ element $\"R\"$ : $\"y%3C=2\"$ }\r
\n" ); document.write( "\n" ); document.write( "Direction of opening: opening down\r
\n" ); document.write( "\n" ); document.write( "Vertex: ( $\"-1\"$ , $\"2\"$ )\r
\n" ); document.write( "\n" ); document.write( "X-intercept; $\"-3%28x%2B1%29%5E2%2B2=0\"$ at $\"x+=+-sqrt%282%2F3%29-1\"$ and $\"x+=+sqrt%282%2F3%29+-+1\"$
\n" ); document.write( "=>( $\"sqrt%282%2F3%29+-+1\"$ , $\"0\"$ ) and ( $\"-sqrt%282%2F3%29-1\"$ , $\"0\"$ )\r
\n" ); document.write( "\n" ); document.write( "Y-intercept: $\"x=0\"$ , $\"y=-3%280%2B1%29%5E2%2B2=-3%2B2=-1\"$ \r
\n" ); document.write( "\n" ); document.write( "=>( $\"0\"$ , $\"-1\"$ )\r
\n" ); document.write( "\n" ); document.write( "Axis of symmetry: $\"x=-1\"$ \r
\n" ); document.write( "\n" ); document.write( "Expansion/compression: stretched by a factor of $\"3\"$ in y-direction\r
\n" ); document.write( "\n" ); document.write( "Congruent to: $\"y+=+-3+x%5E2+-+6+x+-+1\"$ \r
\n" ); document.write( "\n" ); document.write( "MIN/MAX value: max at ( $\"-1\"$ , $\"2\"$ )\r
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\n" ); document.write( "\n" ); document.write( "3. $\"y=%281%2F2%29%28x-2%29%5E2-4+\"$ \r
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\n" ); document.write( " $\"+graph%28600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29%28x-2%29%5E2-4+%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Domain: $\"R\"$ (all real numbers)\r
\n" ); document.write( "\n" ); document.write( "Range:{ $\"y\"$ element $\"R\"$ : $\"y%3E=-4\"$ }\r
\n" ); document.write( "\n" ); document.write( "Direction of opening: $\"up\"$ \r
\n" ); document.write( "\n" ); document.write( "Vertex: ( $\"2\"$ , $\"+-4\"$ )\r
\n" ); document.write( "\n" ); document.write( "X-intercept; ( $\"2%281+-+sqrt%282%29%29\"$ , $\"0\"$ ) and ( $\"2+%281+%2B+sqrt%282%29%29\"$ , $\"0\"$ )\r
\n" ); document.write( "\n" ); document.write( "Y-intercept: ( $\"0\"$ , $\"-4\"$ )\r
\n" ); document.write( "\n" ); document.write( "Axis of symmetry: $\"x=2\"$ \r
\n" ); document.write( "\n" ); document.write( "Expansion/compression: compressed by factor $\"2\"$ in y-direction\r
\n" ); document.write( "\n" ); document.write( "Congruent to: $\"y+=+x%5E2%2F2+-+2x+-+2\"$ \r
\n" ); document.write( "\n" ); document.write( "MIN/MAX value: minimum at ( $\"2\"$ , $\"+-4\"$ )\r
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