document.write( "Question 1190865: Find the equation of a parabola with axis parallel to Ox and passing through (5, 4), (11, 2), and (21, -4). \n" ); document.write( "

Algebra.Com's Answer #823096 by Alan3354(69443) $\"\"$ $\"About$

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Find the equation of a parabola with axis parallel to Ox and passing through
\n" ); document.write( "(5,4), (11,2), and (21,-4).
\n" ); document.write( "If \"parallel to Ox\" means parallel to the x-axis:
\n" ); document.write( "-----------------
\n" ); document.write( "Parabolas parallel to the x-axis have the form:
\n" ); document.write( "x = ay^2 + by + c
\n" ); document.write( "------------
\n" ); document.write( "5 = a*4^2 + b*4 + c at (5,4)
\n" ); document.write( "11= a*2^2 + b*2 + c at (11,2)
\n" ); document.write( "21= a*4^2 + b*-4 + c at (21,-4)
\n" ); document.write( "------
\n" ); document.write( "

\r\n" );
document.write( "16a + 4b + c = 5  Eqn 1\r\n" );
document.write( " 4a + 2b + c = 11 Eqn 2\r\n" );
document.write( "16a - 4b + c = 21 Eqn 3\r\n" );
document.write( "---\r\n" );
document.write( "16a + 4b + c = 5  Eqn 1\r\n" );
document.write( "16a - 4b + c = 21 Eqn 3\r\n" );
document.write( "----------------------------- Add\r\n" );
document.write( "32a + 2c = 26  Eqn A\r\n" );
document.write( "---\r\n" );
document.write( "16a + 4b + c = 5  Eqn 1\r\n" );
document.write( " 8a + 4b + 2c = 22 Eqn 2 times 2\r\n" );
document.write( "----------------------------------------- Subtract\r\n" );
document.write( " 8a - c = -17\r\n" );
document.write( "16a + c = 13  Eqn A divided by 2\r\n" );
document.write( "------------------------------------------ Add\r\n" );
document.write( "24a = -4\r\n" );
document.write( "a = -1/6\r\n" );
document.write( "============\r\n" );
document.write( "16a + c = 13  Eqn A divided by 2\r\n" );
document.write( "-8/3 + c = 13\r\n" );
document.write( "c = 47/3\r\n" );
document.write( "=================\r\n" );
document.write( " 4a + 2b + c = 11 Eqn 2\r\n" );
document.write( "-2/3 + 2b + 47/3 = 11\r\n" );
document.write( "2b = -4\r\n" );
document.write( "b = -2\r\n" );
document.write( "=================\r\n" );
document.write( "--> x = -y^2/6 - 2y + 47/3\r\n" );
document.write( "

\n" ); document.write( "

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