document.write( "Question 457082: whats the equation of the parabo0la vertext at (-4,5) passes thru (0,9) \n" ); document.write( "

Algebra.Com's Answer #313654 by Edwin McCravy(20060) $\"\"$ $\"About$

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whats the equation of the parabola vertext at (-4,5) passes thru (0,9)
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document.write( "Two ways:\r\n" );
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document.write( "1. If you've had this equation for a parabola\r\n" );
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document.write( "(x - h)² = 4p(y - k)\r\n" );
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document.write( "2. If you've had this equation for a parabola\r\n" );
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document.write( "y = a(x - h)² + k\r\n" );
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document.write( "I'll do it both ways.  Either way (h,k) = (-4,5), (x,y) = (0,9)\r\n" );
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document.write( "1. If you've had this equation for a parabola\r\n" );
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document.write( "   (x - h)² = 4p(y - k)\r\n" );
document.write( "(0 - (-4))² = 4p(9 - 5)\r\n" );
document.write( "  (0 + 4)²  = 4p(4)\r\n" );
document.write( "         4² = 16p\r\n" );
document.write( "         16 = 16p\r\n" );
document.write( "          1 = p\r\n" );
document.write( "Rewrite original:\r\n" );
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document.write( "   (x - h)² = 4p(y - k)\r\n" );
document.write( "(x - (-4))² = 4(1)(y - 5)\r\n" );
document.write( "   (x + 4)² = 4(y - 5)\r\n" );
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document.write( "--------------------------------\r\n" );
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document.write( "2. If you've had this equation for a parabola\r\n" );
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document.write( "   y = a(x - h)² + k\r\n" );
document.write( "   9 = a(0 - (-4))² + 5\r\n" );
document.write( "   9 = a(0 + 4)² + 5\r\n" );
document.write( "   9 = a(4)² + 5\r\n" );
document.write( "   9 = a(16) + 5\r\n" );
document.write( "   9 = 16a + 5\r\n" );
document.write( "   4 = 16a\r\n" );
document.write( "4/16 = a\r\n" );
document.write( " 1/4 = a\r\n" );
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document.write( "Rewrite original equation\r\n" );
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document.write( "   y = (1/4)(x - (-4))² + 5\r\n" );
document.write( "   y = (1/4)(x + 4)² + 5\r\n" );
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document.write( "-----------------------------\r\n" );
document.write( "Either way the graph is\r\n" );
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document.write( "Edwin

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