document.write( "Question 336452: what is the vertex of a parabola that is pointing downward and contains the points (-2,2), (0,1), and (1,2.5). \n" ); document.write( "

Algebra.Com's Answer #241765 by Fombitz(32388) $\"\"$ $\"About$

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The general equation for a parabola is $\"y=ax%5E2%2Bbx%2Bc\"$
\n" ); document.write( "Solve for $\"a\"$ , $\"b\"$ , and $\"c\"$ using the points ( $\"-2\"$ , $\"2\"$ ), ( $\"0\"$ , $\"1\"$ ), and ( $\"1\"$ , $\"2.5\"$ ).
\n" ); document.write( " $\"+2=a%28-2%29%5E2%2Bb%28-2%29%2Bc\"$
\n" ); document.write( " $\"+4a-2b%2Bc=2\"$
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\n" ); document.write( " $\"+1=a%280%29%5E2%2Bb%280%29%2Bc\"$
\n" ); document.write( " $\"+highlight_green%28c=1%29\"$
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\n" ); document.write( " $\"+5%2F2=a%281%29%5E2%2Bb%281%29%2Bc\"$
\n" ); document.write( " $\"+a%2Bb%2Bc=5%2F2\"$
\n" ); document.write( "Simplify with $\"c=1\"$
\n" ); document.write( " $\"4a-2b%2B1=2\"$
\n" ); document.write( "1. $\"4a-2b=1\"$
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\n" ); document.write( " $\"a%2Bb%2B1=5%2F2\"$
\n" ); document.write( " $\"a%2Bb=3%2F2\"$
\n" ); document.write( "2. $\"2a%2B2b=3\"$
\n" ); document.write( "Add eq. 1 and eq. 2 to eliminate $\"b\"$ ,
\n" ); document.write( " $\"4a-2b%2B2a%2B2b=1%2B3\"$
\n" ); document.write( " $\"6a=4\"$
\n" ); document.write( " $\"highlight_green%28a=2%2F3%29\"$
\n" ); document.write( "Then from eq. 3,
\n" ); document.write( " $\"2a%2B2b=3\"$
\n" ); document.write( " $\"4%2F3%2B2b=9%2F3\"$
\n" ); document.write( " $\"2b=5%2F3\"$
\n" ); document.write( " $\"highlight_green%28b=5%2F6%29\"$
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\n" ); document.write( " $\"y=%282%2F3%29x%5E2%2B%285%2F6%29x%2B1\"$
\n" ); document.write( "Complete the square to put the equation into vertex form, $\"y=a%28x-h%29%5E2%2Bk\"$ where ( $\"h\"$ , $\"k\"$ ) is the vertex.
\n" ); document.write( " $\"y=%282%2F3%29x%5E2%2B%285%2F6%29x%2B1\"$
\n" ); document.write( " $\"y=%282%2F3%29%28x%5E2%2B%285%2F4%29x%29%2B1\"$
\n" ); document.write( " $\"y=%282%2F3%29%28x%5E2%2B%285%2F4%29x%2B25%2F64%29%2B1-%282%2F3%29%2825%2F64%29\"$
\n" ); document.write( " $\"y=%282%2F3%29%28x%2B5%2F8%29%5E2%2B96%2F96-25%2F96\"$
\n" ); document.write( " $\"y=%282%2F3%29%28x%2B5%2F8%29%5E2%2B71%2F96\"$
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\n" ); document.write( "Vertex:( $\"-5%2F8\"$ , $\"71%2F96\"$ )
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\n" ); document.write( "The parabola opens upwards. \n" ); document.write( "

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