document.write( "Question 173: how do I find a parabola that passes through the points: (2,-3),(-2,9), and (1,3/2)? \n" ); document.write( "

Algebra.Com's Answer #152 by AnlytcPhil(1806) $\"\"$ $\"About$

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How do I find a parabola that passes through the points:
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document.write( "(2,-3),(-2,9), and (1,3/2)? I can not find any examples in my book.
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document.write( "Start with the general equation of a parabola:
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document.write( "                  y = Ax² + Bx + C 
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document.write( "Substitute in the point (2,-3), that is, substitute 2 for x and -3 for y
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document.write( "                 -3 = A(2)² + B(2) + C
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document.write( "                 -3 = A(4) + 2B + C
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document.write( "                 -3 = 4A + 2B + C
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document.write( "(1)     4A + 2B + C = -3
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document.write( " Substitute in the point (-2,9), that is, substitute -2 for x and 9 for y
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document.write( "                  y = Ax² + Bx + C
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document.write( "                  9 = A(-2)² + B(-2) + C
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document.write( "                  9 = A(4) - 2B + C
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document.write( "                  9 = 4A - 2B + C
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document.write( "(2)     4A - 2B + C = 9
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document.write( "Substitute in the point (1,3/2), that is, substitute -2 for x and 9 for y
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document.write( "                  y = Ax² + Bx + C
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document.write( "                3/2 = A(1)² + B(1) + C
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document.write( "                3/2 = A(1) + B + C
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document.write( "                3/2 = A + B + C
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document.write( "(3)       A + B + C = 3/2
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document.write( "So you have this system of equations:
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document.write( "(1)     4A + 2B + C = -3
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document.write( "(2)     4A - 2B + C = 9
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document.write( "(3)       A + B + C = 3/2\r
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document.write( "Do you know how to solve this system? I will assume you do.
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document.write( "If you don't, post again.\r
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document.write( "Answers:   A = -1/2, B = -3,  C = 5\r
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document.write( "So substitute these values into the general equation\r
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document.write( "                  y = Ax² + Bx + C
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document.write( "and get
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document.write( "                  y = -1/2x² - 3x + 5\r
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document.write( "Here's the graph:
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document.write( " \r
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document.write( "Edwin  \n" );
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