document.write( "Question 1012541: find a quadratic model in standard form for this set of values:
\n" ); document.write( "(0,0), (1,-5), (2,0) \n" ); document.write( "

Algebra.Com's Answer #628508 by Fombitz(32388) $\"\"$ $\"About$

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Use the general form of a quadratic,
\n" ); document.write( " $\"y=ax%5E2%2Bbx%2Bc\"$
\n" ); document.write( "(0,0)
\n" ); document.write( " $\"0=a%280%29%5E2%2Bb%280%29%2Bc\"$
\n" ); document.write( " $\"c=0\"$
\n" ); document.write( "(1,-5)
\n" ); document.write( " $\"-5=a%281%29%5E2%2Bb%281%29\"$
\n" ); document.write( "1. $\"a%2Bb=-5\"$
\n" ); document.write( "(2,0)
\n" ); document.write( " $\"0=a%282%29%5E2%2Bb%282%29\"$
\n" ); document.write( " $\"4a%2B2b=0\"$
\n" ); document.write( "2. $\"2a%2Bb=0\"$
\n" ); document.write( "Subtracting eq. 1 from eq. 2,
\n" ); document.write( " $\"2a%2Bb-%28a%2Bb%29=0-%28-5%29\"$
\n" ); document.write( " $\"2a%2Bb-a-b=5\"$
\n" ); document.write( " $\"a=5\"$
\n" ); document.write( "Then from eq. 2,
\n" ); document.write( " $\"2%285%29%2Bb=0\"$
\n" ); document.write( " $\"10%2Bb=0\"$
\n" ); document.write( " $\"b=-10\"$
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\n" ); document.write( " $\"y=5x%5E2-10x\"$
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.\r
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