document.write( "Question 1000034: How to find the unknown coefficients when the vertex is given: (3,-4)\r
\n" ); document.write( "\n" ); document.write( "y=x^2 + bx + c \n" ); document.write( "

Algebra.Com's Answer #617536 by jim_thompson5910(35256) $\"\"$ $\"About$

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y=x^2 + bx + c has a = 1\r
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\n" ); document.write( "\n" ); document.write( "\"the vertex is given: (3,-4) \"
\n" ); document.write( "(h,k) = (3,-4)
\n" ); document.write( "h = 3\r
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\n" ); document.write( "\n" ); document.write( "h = -b/(2a)
\n" ); document.write( "3 = -b/(2*1) ... plug in h = 3 and a = 1
\n" ); document.write( "3 = -b/2
\n" ); document.write( "3*2 = -b
\n" ); document.write( "6 = -b
\n" ); document.write( "-b = 6
\n" ); document.write( "b = -6\r
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\n" ); document.write( "\n" ); document.write( "y=x^2 + bx + c
\n" ); document.write( "y=x^2 - 6x + c ... plug in b = -6
\n" ); document.write( "-4=3^2 - 6(3) + c ... plug in (x,y) = (3,-4)
\n" ); document.write( "-4 = 9-18+c
\n" ); document.write( "-4 = -9+c
\n" ); document.write( "-4+9 = -9+c+9
\n" ); document.write( "5 = c
\n" ); document.write( "c = 5\r
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\n" ); document.write( "\n" ); document.write( "So the equation is y = x^2 - 6x + 5 \n" ); document.write( "

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