document.write( "Question 1161075: Find the quadratic polynomial whose graph passes through the points (1,14) (2,28) (3,48) \n" ); document.write( "

Algebra.Com's Answer #784511 by MathLover1(20850) $\"\"$ $\"About$

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$\"y=ax%5E2%2Bbx%2Bc\"$ use given point ( $\"1\"$ , $\"14\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"14=a%2A1%5E2%2Bb%2A1%2Bc\"$
\n" ); document.write( " $\"14=a%2Bb%2Bc\"$ ......solve for $\"c\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"c=14-a-b\"$ .........eq.1\r
\n" ); document.write( "\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$ use given point ( $\"2\"$ , $\"28\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"28=a%2A2%5E2%2Bb%2A2%2Bc\"$
\n" ); document.write( " $\"28=4a%2B2b%2Bc\"$ ......solve for $\"c\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"c=28-4a-2b\"$ .........eq.2\r
\n" ); document.write( "\n" ); document.write( "from eq.1 and eq.2 we have\r
\n" ); document.write( "\n" ); document.write( " $\"14-a-b=28-4a-2b\"$ .....solve for $\"b\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2b-b=28-4a%2Ba-14\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"b=14-3a\"$ .........eq.3\r
\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( " $\"c=14-a-b\"$ .........eq.1, substitute $\"b\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"c=14-a-%2814-3a%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"c=14-a-14%2B3a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"c=2a\"$ ...............eq.4\r
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\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$ use given point ( $\"3\"$ , $\"48\"$ ), substitute $\"b\"$ from eq.3 and $\"c\"$ from eq.4\r
\n" ); document.write( "\n" ); document.write( " $\"48=a%2A3%5E2%2B%2814-3a%29%2A3%2B2a\"$ ........solve for $\"a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"48=9a%2B42-9a%2B2a\"$ .....simplify\r
\n" ); document.write( "\n" ); document.write( " $\"48=42%2B2a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"48-42=2a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2a=6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28a=3%29\"$ \r
\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( " $\"b=14-3a\"$ .........eq.3, substitute $\"a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"b=14-3%2A3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28b=5%29\"$ \r
\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( " $\"c=2a\"$ ...............eq.4, substitute $\"a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"c=2%2A3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28c=6%29\"$ \r
\n" ); document.write( "\n" ); document.write( "your equation is:\r
\n" ); document.write( "\n" ); document.write( " $\"y=3x%5E2%2B5x%2B6\"$ \r
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