document.write( "Question 79052: I need help to write an equation of a quadratic function whose graph is a parabola that has a vertex (-3,7) and that passes through the origin. Please. \n" ); document.write( "
Algebra.Com's Answer #56749 by Edwin McCravy(20055)\"\" \"About 
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document.write( "I need help to write an equation of a quadratic function \r\n" );
document.write( "whose graph is a parabola that has a vertex (-3,7) and \r\n" );
document.write( "that passes through the origin. Please.\r\n" );
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document.write( "The standard form of a parabola with vertex (h,k) is\r\n" );
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document.write( "y = a(x - h)² + k\r\n" );
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document.write( "where (h, k) is its vertex.\r\n" );
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document.write( "Since its vertex is (-3,7) we substitute -3 for h and 7 fo k.\r\n" );
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document.write( "y = a(x - (-3) )² + 7\r\n" );
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document.write( "y = a(x + 3)² + 7\r\n" );
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document.write( "Since it passes through the origin, which is the point\r\n" );
document.write( "(x,y) = (0,0), if we substitute that point into the equation,\r\n" );
document.write( "the equation must be satisfied, So we substitute that point \r\n" );
document.write( "by substituting 0 for x and 0 fot y:\r\n" );
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document.write( "y = a(x + 3)² + 7\r\n" );
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document.write( "0 = a(0 + 3)² + 7\r\n" );
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document.write( "0 = a(3)² + 7\r\n" );
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document.write( "0 = a(9) + 7\r\n" );
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document.write( "0 = 9a + 7\r\n" );
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document.write( "add -9a to both sides\r\n" );
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document.write( "-9a = 7\r\n" );
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document.write( "divide both sides by -9\r\n" );
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document.write( "  a = -7/9\r\n" );
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document.write( "So now we go back to \r\n" );
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document.write( "y = a(x + 3)² + 7\r\n" );
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document.write( "and replace a by (-7/9)\r\n" );
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document.write( "y = (-7/9)(x + 3)² + 7\r\n" );
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document.write( "Your teacher may accept it that way, or you\r\n" );
document.write( "can clear of fractions  by multiplying \r\n" );
document.write( "through by the LCD = 9\r\n" );
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document.write( "9y = -7(x + 3)² + 63\r\n" );
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document.write( "9y = -7(x + 3)(x + 3) + 63\r\n" );
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document.write( "9y = -7(x² + 3x + 3x + 9) + 63\r\n" );
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document.write( "9y = -7(x² + 6x + 9) + 63\r\n" );
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document.write( "9y = -7x² - 42x - 63 + 63\r\n" );
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document.write( "9y = -7x² - 42x, which you could write as 7x² + 42x + 9y = 0\r\n" );
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document.write( "or if you didn't want to do that you could\r\n" );
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document.write( "Factor out -7x on the right\r\n" );
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document.write( "9y = -7x(x + 6)\r\n" );
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document.write( "Divide through by 9\r\n" );
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document.write( " y = -7(x + 6)/9\r\n" );
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document.write( "There are lots of ways you could leave the answer.\r\n" );
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document.write( "Edwin

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