document.write( "Question 522222: Please help! I would really appreciate it.\r
\n" ); document.write( "\n" ); document.write( "I have to write these equations in vertex form and tell whether they open up or down.\r
\n" ); document.write( "\n" ); document.write( "1.The vertex of the parabola is the (2,5)Point T (3,0) lies on the graph of the parabola.\r
\n" ); document.write( "\n" ); document.write( "2.The vertex of the parabola is the (-3,-5. Point G (1,6) lies on the graph of the parabola) \n" ); document.write( "

Algebra.Com's Answer #346776 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
1. The vertex of the parabola is the (2,5)Point T (3,0) lies on the graph of the parabola.
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document.write( "We plot the vertex (2,5) and the point T(3,0).\r\n" );
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document.write( "Next we plot the line (axis) of symmetry, which is the vertical line \r\n" );
document.write( "that goes through the vertex, the green line below:\r\n" );
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document.write( "On the other side (left side) of the green line of symmetry, plot\r\n" );
document.write( "the point that is just as far to the left of the green line and on \r\n" );
document.write( "the same level as T(3,0), which is this one:\r\n" );
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document.write( "We can sketch in the graph as this:\r\n" );
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document.write( "We see that the parabola opens downward, and therefore we suspect\r\n" );
document.write( "that \"a\" is a negative number.\r\n" );
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document.write( "The equation of the parabola is of the form\r\n" );
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document.write( "y = a(x-h)² + k \r\n" );
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document.write( "where the vertex is (h,k), so (h,k) = (2,5), so we substitute h=2 and k=5.\r\n" );
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document.write( "y = a(x-2)²+5\r\n" );
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document.write( "Now all we lack is the value of \"a\".  \r\n" );
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document.write( "Since the parabola contains the point T(3,0) we can substitute\r\n" );
document.write( "x=3, y=0, and the equation will be true, so:\r\n" );
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document.write( "0 = a(3-2)²+5\r\n" );
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document.write( "0 = a(1)² + 5\r\n" );
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document.write( "0 = a + 5\r\n" );
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document.write( "-5 = a\r\n" );
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document.write( "Substituting -5 for a, the equation of the parabola\r\n" );
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document.write( "y = a(x-2)²+5\r\n" );
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document.write( "is now complete as\r\n" );
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document.write( "y = -5(x-2)²+5\r\n" );
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\n" ); document.write( "2. The vertex of the parabola is the (-3,-5). Point G(1,6) lies on the graph of the parabola)
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document.write( "We plot the vertex (-3,-5) and the point G(1,6).\r\n" );
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document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next we plot the line (axis) of symmetry, which is the vertical line \r\n" );
document.write( "that goes through the vertex, the green line below:\r\n" );
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document.write( "\r\n" );
document.write( "\r\n" );
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document.write( " \r\n" );
document.write( "On the other side (left side) of the green line of symmetry, plot\r\n" );
document.write( "the point that is just as far to the left of the green line and on \r\n" );
document.write( "the same level as G(1,6), which is this one:\r\n" );
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document.write( "We can sketch in the graph as this parabola:\r\n" );
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document.write( "We see that the parabola opens upward, and therefore we suspect\r\n" );
document.write( "that \"a\" is a positive number.\r\n" );
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document.write( "The equation of the parabola is of the form\r\n" );
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document.write( "y = a(x-h)² + k \r\n" );
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document.write( "where the vertex is (h,k), so (h,k) = (-3,-5), so we substitute h=-3 and k=-5.\r\n" );
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document.write( "y = a(x-(-3))²+(-5)\r\n" );
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document.write( "y = a(x+3)²-5\r\n" );
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document.write( "Now all we lack is the value of \"a\".  \r\n" );
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document.write( "Since the parabola contains the point G(1,6) we can substitute\r\n" );
document.write( "x=1, y=6, and the equation will be true, so:\r\n" );
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document.write( "6 = a(1+3)²-5\r\n" );
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document.write( "6 = a(4)² - 5\r\n" );
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document.write( "6 = 16a - 5\r\n" );
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document.write( "11 = 16a\r\n" );
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document.write( " = a\r\n" );
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document.write( "Substituting  for a, the equation of the parabola\r\n" );
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document.write( "y = (x+3)²-5\r\n" );
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document.write( "Edwin

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