document.write( "Question 1077218: What's the equation of the parabola $\"+y+=+ax%5E2+%2B+bx+%2B+c+\"$ which passes through the points of (0, 3), (1,4), and (2, 3)?\r
\n" ); document.write( "\n" ); document.write( "A.) y = -(Ľ)x2 + (˝)x + 3
\n" ); document.write( "B.) y = -(⅔)x2 + (5/3)x + 3
\n" ); document.write( "C.) y = 2x2 - 13x + 21
\n" ); document.write( "D.) y = -x2 + 2x + 3 \n" ); document.write( "

Algebra.Com's Answer #691765 by MathLover1(20849) $\"\"$ $\"About$

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\n" ); document.write( "What's the equation of the parabola $\"y=ax%5E2%2Bbx%2Bc\"$ which passes through the points of ( $\"0\"$ , $\"3\"$ ), ( $\"1\"$ , $\"4\"$ ), and ( $\"2\"$ , $\"+3\"$ )? \r
\n" ); document.write( "\n" ); document.write( "use given points to find $\"a\"$ , $\"b\"$ ,and $\"c\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$ ...............for point ( $\"0\"$ , $\"3\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"3=a%2A0%5E2%2Bb%2A0%2Bc\"$
\n" ); document.write( " $\"3=c\"$ .........eq.1\r
\n" ); document.write( "\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$ ............for $\"3=c\"$ and ( $\"1\"$ , $\"4\"$ )\r
\n" ); document.write( "\n" ); document.write( " $\"4=a%2A1%5E2%2Bb%2A1%2B3\"$
\n" ); document.write( " $\"4=a%2Bb%2B3\"$
\n" ); document.write( " $\"1=a%2Bb\"$ .........solve for $\"a\"$
\n" ); document.write( " $\"a=1-b\"$ ..........eq.2\r
\n" ); document.write( "\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$ ............ $\"3=c\"$ , $\"a=1-b\"$ , and ( $\"2\"$ , $\"3\"$ )
\n" ); document.write( " $\"3=%281-b%292%5E2%2Bb%2A2%2B3\"$
\n" ); document.write( " $\"3-3=%281-b%294%2B2b\"$
\n" ); document.write( " $\"0=4-4b%2B2b\"$
\n" ); document.write( " $\"0=4-2b\"$
\n" ); document.write( " $\"2b=4\"$
\n" ); document.write( " $\"b=2\"$ ........eq.3\r
\n" ); document.write( "\n" ); document.write( "find $\"a\"$
\n" ); document.write( " $\"a=1-b\"$ ..........eq.2
\n" ); document.write( " $\"a=1-2\"$
\n" ); document.write( " $\"a=-1\"$ \r
\n" ); document.write( "\n" ); document.write( "so, your equation is:\r
\n" ); document.write( "\n" ); document.write( " $\"y=-x%5E2%2B2x%2B3\"$ \r
\n" ); document.write( "\n" ); document.write( "and your answer is: D.) $\"y=-x%5E2%2B2x%2B3\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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