document.write( "Question 1127572: Write the equation of a parabola with x-intercepts at (3, 0) and (9, 0) that passes through the point (10,-7)
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Algebra.Com's Answer #744010 by greenestamps(13200)\"\" \"About 
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\n" ); document.write( "Answer the question using the symmetry of the parabola and the vertex form of the equation of a parabola,

\n" ); document.write( "\"y-k+=+a%28x-h%29%5E2\" where (h,k) is the vertex.

\n" ); document.write( "(1) With x-intercepts 3 and 9, the axis of symmetry is x=6, so the equation is of the form

\n" ); document.write( "\"y+=+a%28x-6%29%5E2%2Bk\"

\n" ); document.write( "(2) Use one of the x-intercepts and the third point in that equation to find the value of a:
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document.write( "    (9,0)   -->   0 = a(3^2)+k   9a+k =  0\r\n" );
document.write( "    (10,-7) -->  -7 = a(4^2)+k  16a+k = -7\r\n" );
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document.write( "                                 7a   = -7\r\n" );
document.write( "                                    a = -1


\n" ); document.write( "The equation is now of the form

\n" ); document.write( "\"y+=+-1%28x-6%29%5E2%2Bk\"

\n" ); document.write( "(3) Use either x-intercept to find k:

\n" ); document.write( "\"0+=+-1%289%29%2Bk\"
\n" ); document.write( "\"k+=+9\"

\n" ); document.write( "We are done....

\n" ); document.write( "ANSWER: \"y+=+-1%28x-6%29%5E2%2B9\"
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