document.write( "Question 1002751: Find an equation in the form y=ax^2+bx+c for the parabola passing through the points (3,-22) (1,4) (2,-4) \n" ); document.write( "

Algebra.Com's Answer #619624 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$ for the parabola passing through the points ( $\"3\"$ , $\"-22\"$ ) ( $\"1\"$ , $\"4\"$ ) ( $\"2\"$ , $\"-4\"$ )\r
\n" ); document.write( "\n" ); document.write( "use given points to set up the system and find $\"a\"$ , $\"b\"$ and $\"c\"$ \r
\n" ); document.write( "\n" ); document.write( "( $\"3\"$ , $\"-22\"$ ):\r
\n" ); document.write( "\n" ); document.write( " $\"-22=a%2A3%5E2%2Bb%2A3%2Bc\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-22=9a%2B3b%2Bc\"$ .....eq.1\r
\n" ); document.write( "\n" ); document.write( " ( $\"1\"$ , $\"4\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"4=a%2A1%5E2%2Bb%2A1%2Bc\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"4=a%2Bb%2Bc\"$ .....eq.2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "( $\"2\"$ , $\"-4\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"-4=a%2A2%5E2%2Bb%2A2%2Bc\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-4=4a%2B2b%2Bc\"$ .....eq.3\r
\n" ); document.write( "\n" ); document.write( "so, the system is:\r
\n" ); document.write( "\n" ); document.write( " $\"-22=9a%2B3b%2Bc\"$ .....eq.1
\n" ); document.write( " $\"4=a%2Bb%2Bc\"$ .....eq.2
\n" ); document.write( " $\"-4=4a%2B2b%2Bc\"$ .....eq.3
\n" ); document.write( "----------------------------
\n" ); document.write( "start with\r
\n" ); document.write( "\n" ); document.write( " $\"-22=9a%2B3b%2Bc\"$ .....eq.1
\n" ); document.write( " $\"4=a%2Bb%2Bc\"$ .....eq.2
\n" ); document.write( "-----------------------------subtract eq.1 from eq.2\r
\n" ); document.write( "\n" ); document.write( " $\"4-%28-22%29=a%2Bb%2Bc-9a-3b-c\"$
\n" ); document.write( " $\"4%2B22=-8a-2b\"$
\n" ); document.write( " $\"26=-8a-2b\"$ .....both sides divide by $\"2\"$
\n" ); document.write( " $\"13=-4a-b\"$ .....solve for $\"b\"$
\n" ); document.write( " $\"b=-4a-13\"$ ...............1a\r
\n" ); document.write( "\n" ); document.write( "do same with eq.2 and eq.3\r
\n" ); document.write( "\n" ); document.write( " $\"4=a%2Bb%2Bc\"$ .....eq.2
\n" ); document.write( " $\"-4=4a%2B2b%2Bc\"$ .....eq.3
\n" ); document.write( "----------------------------subtract eq.2 from eq.3
\n" ); document.write( " $\"-4-4=4a%2B2b%2Bc-a-b-c\"$
\n" ); document.write( " $\"-8=3a%2Bb\"$
\n" ); document.write( " $\"b=-8-3a\"$ ........2a\r
\n" ); document.write( "\n" ); document.write( "from 1a and 2a we have:\r
\n" ); document.write( "\n" ); document.write( " $\"-4a-13=-8-3a\"$ ........solve for $\"a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"8-13=4a-3a\"$
\n" ); document.write( " $\"highlight%28a=-5%29\"$ \r
\n" ); document.write( "\n" ); document.write( "go to $\"b=-8-3a\"$ ........2a, substitute $\"-5\"$ for $\"a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"b=-8-3%28-5%29\"$
\n" ); document.write( " $\"b=-8%2B15\"$
\n" ); document.write( " $\"highlight%28b=7%29\"$ \r
\n" ); document.write( "\n" ); document.write( "go to $\"4=a%2Bb%2Bc\"$ .....eq.2, substitute $\"-5\"$ for $\"a\"$ and $\"7\"$ for $\"b\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"4=-5%2B7%2Bc\"$
\n" ); document.write( " $\"4=2%2Bc\"$
\n" ); document.write( " $\"c=4-2\"$
\n" ); document.write( " $\"highlight%28c=2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "so, your equation is: $\"y=-5x%5E2%2B7x%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( "see it and given points on the graph:
\n" ); document.write( "( $\"3\"$ , $\"-22\"$ ) ( $\"1\"$ , $\"4\"$ ) ( $\"2\"$ , $\"-4\"$ )\r
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );