document.write( "Question 318422: Find the equation of a parabola that passes through the points (-2,3), (-1,1) and (1,9). \n" ); document.write( "

Algebra.Com's Answer #227942 by Fombitz(32388) $\"\"$ $\"About$

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The general equation for a parabola is,
\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$
\n" ); document.write( "1.(-2,3): $\"3=4a-2b%2Bc\"$
\n" ); document.write( "2.(-1,1): $\"1=+a+-+b+%2B+c\"$
\n" ); document.write( "3.(1,9): $\"9=+a+%2B+b+%2B+c+\"$
\n" ); document.write( "Solve for a,b,c using elimination, substitution, or matrix methods.
\n" ); document.write( "Solve for b by subtracting eq. 2 and eq. 3,
\n" ); document.write( " $\"a-b%2Bc-a-b-c=1-9\"$
\n" ); document.write( " $\"-2b=-8\"$
\n" ); document.write( " $\"highlight%28b=4%29\"$
\n" ); document.write( "Then substituting for b, subtract eq. 3 from eq. 1,
\n" ); document.write( " $\"4a+-+8+%2B+c+-+a+-+4+-+c=3+-+9\"$
\n" ); document.write( " $\"3a-12=-6\"$
\n" ); document.write( " $\"3a=6\"$
\n" ); document.write( " $\"highlight%28a=2%29\"$
\n" ); document.write( "Finally from eq. 3,
\n" ); document.write( " $\"2%2B4%2Bc=9\"$
\n" ); document.write( " $\"highlight%28c=3%29\"$
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\n" ); document.write( " $\"highlight_green%28y=2x%5E2%2B4x%2B3%29\"$ \n" ); document.write( "

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