document.write( "Question 120056: This question comes from a quiz that my teacher gives us. I've worked on it for two weeks and can not seem to get the answer right. Please help!\r
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Algebra.Com's Answer #88018 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
This question comes from a quiz that my teacher gives us. I've worked on it for two weeks and can not seem to get the answer right. Please help!
\n" ); document.write( "Given y = -2(x - 1)^2 + 3,describe the transformations on y=x^2 that would produce y = -2(x - 1)^2 + 3. Write the equation in standard form.
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document.write( "You must start with y = x² and end up with y = -2(x - 1)² + 3\r\n" );
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document.write( "Start with this red equation: \r\n" );
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document.write( "y = x²\r\n" );
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document.write( "which has this red curve as its graph:\r\n" );
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document.write( "\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2%29\"\r\n" );
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document.write( "Then you multiply the right side of the red\r\n" );
document.write( "equation by 2 to get the green equation:\r\n" );
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document.write( "y = 2x²\r\n" );
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document.write( "That stretches the red curve vertically by a \r\n" );
document.write( "factor of 2, giving the green curve below.\r\n" );
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document.write( "\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2%2C2x%5E2%29\"\r\n" );
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document.write( "Then you multiply the right side of the green\r\n" );
document.write( "equation by -1 to get\r\n" );
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document.write( "y = -2x²\r\n" );
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document.write( "That reflects the green curve across the x-axis, \r\n" );
document.write( "giving the blue curve below:\r\n" );
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document.write( "\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C0%2C2x%5E2%2C-2x%5E2%29\"\r\n" );
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document.write( "Then you replace x by (x - 1) in the right side of\r\n" );
document.write( "the blue equation to get\r\n" );
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document.write( "y = -2(x - 1)²\r\n" );
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document.write( "That shifts the blue graph 1 unit right, giving the\r\n" );
document.write( "purple curve below:\r\n" );
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document.write( "\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C0%2C0%2C-2x%5E2%2C-2%28x-1%29%5E2%29\"\r\n" );
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document.write( "Finally you add 3 to the right side of the purple equation\r\n" );
document.write( "to get\r\n" );
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document.write( "y = -2(x - 1)² + 3 \r\n" );
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document.write( "That shifts the purple graph 3 units upward, giving the\r\n" );
document.write( "light blue graph below:\r\n" );
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document.write( "That light blue graph is hard to see, so here it is in red:\r\n" );
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document.write( "\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-2%28x-1%29%5E2%2B3%29\" \r\n" );
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document.write( "But as you see the transformations in order were:\r\n" );
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document.write( "1. Stretch vertically by a factor of 2.  (Multiply right side by 2)\r\n" );
document.write( "2. Reflect across the x-axis.  (Multiply right side by -1)\r\n" );
document.write( "3. Shift right 1 unit. [Replace x by (x-1) ]\r\n" );
document.write( "4. Shift up 3 units. {Add 3 to the right side.]\r\n" );
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document.write( "Edwin
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