document.write( "Question 358553: Find the equation of the parabola passing through the given points (1,3)(2,3)(3,5). Show the system of equations containing the 3 points and then solve for the constants, a,b,and c. Then, show the standard form equation of the parabola. \n" ); document.write( "

Algebra.Com's Answer #255915 by Fombitz(32388) $\"\"$ $\"About$

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Since ( $\"1\"$ , $\"3\"$ ) and ( $\"2\"$ , $\"3\"$ ) share a y-value, they are on opposite sides of the vertex.
\n" ); document.write( "The $\"x\"$ coordinate of the vertex is $\"%281%2B2%29%2F2=3%2F2\"$
\n" ); document.write( "Use the vertex form,
\n" ); document.write( " $\"y=a%28x-h%29%5E2%2Bk\"$
\n" ); document.write( " $\"y=a%28x-3%2F2%29%5E2%2Bk\"$
\n" ); document.write( "Use your points to solve for $\"a\"$ and $\"k\"$ .
\n" ); document.write( " $\"3=a%281-3%2F2%29%5E2%2Bk\"$
\n" ); document.write( " $\"3=a%281%2F4%29%2Bk\"$
\n" ); document.write( "1. $\"a%2B4k=12\"$
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\n" ); document.write( " $\"5=a%283-3%2F2%29%5E2%2Bk\"$
\n" ); document.write( " $\"5=a%289%2F4%29%2Bk\"$
\n" ); document.write( "2. $\"9a%2B4k=20\"$
\n" ); document.write( "Subtract eq. 1 from eq. 2,
\n" ); document.write( " $\"9a%2B4k-a-4k=20-12\"$
\n" ); document.write( " $\"8a=8\"$
\n" ); document.write( " $\"highlight_green%28a=1%29\"$
\n" ); document.write( "Then use either equation to solve for $\"k\"$ .
\n" ); document.write( " $\"1%2B4k=12\"$
\n" ); document.write( " $\"4k=11\"$
\n" ); document.write( " $\"highlight_green%28k=11%2F4%29\"$
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\n" ); document.write( " $\"y=a%28x-3%2F2%29%5E2%2Bk\"$
\n" ); document.write( " $\"y=%28x-3%2F2%29%5E2%2B11%2F4\"$
\n" ); document.write( " $\"y=%28x%5E2-3x%2B9%2F4%29%2B11%2F4\"$
\n" ); document.write( " $\"highlight%28y=x%5E2-3x%2B5%29\"$
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