document.write( "Question 1124651: Find the quadratic equation function that has the given vertex and goes through the given point. Vertex(1,3), point (-2,0) f(x) = \n" ); document.write( "
Algebra.Com's Answer #740980 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
The form is:
\n" ); document.write( "\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"
\n" ); document.write( "The x-value of the vertex is at
\n" ); document.write( "\"+x%5Bv%5D+=+-b%2F%282a%29+\"
\n" ); document.write( "Given: \"x%5Bv%5D+=+1\"
\n" ); document.write( "\"+-b%2F%282a%29+=+1+\"
\n" ); document.write( "\"+b+=+-2a+\"
\n" ); document.write( "Now I can say:
\n" ); document.write( "\"+3+=+a%2A1%5E2+%2B+%28-2a%29%2A1+%2B+c+\"
\n" ); document.write( "\"+c+=+a+%2B+3+\"
\n" ); document.write( "————————
\n" ); document.write( "( -2, 0 )
\n" ); document.write( "\"+y+=+a%2Ax%5E2+%2B+%28-2a%29%2Ax+%2B+a+%2B+3+\"
\n" ); document.write( "\"+0+=+a%2A%28-2%29%5E2+%2B+%28-2a%29%2A%28-2%29+%2B+a+%2B+3+\"
\n" ); document.write( "\"+0+=+4a+%2B+4a+%2B+a+%2B+3+\"
\n" ); document.write( "\"+0+=+9a+%2B+3+\"
\n" ); document.write( "\"+a+=+-1%2F3+\"
\n" ); document.write( "\"+-2a+=+-2%2A%28-1%2F3%29+\"
\n" ); document.write( "\"+-2a+=+2%2F3+\"
\n" ); document.write( "\"+a+%2B+3+=+8%2F3+\"
\n" ); document.write( "—————————————————-
\n" ); document.write( "\"+y+=+%28-1%2F3%29%2Ax%5E2+%2B+%282%2F3%29%2Ax+%2B+8%2F3+\"
\n" ); document.write( "—————————————————-
\n" ); document.write( "Check:
\n" ); document.write( "(1,3)
\n" ); document.write( "\"+3+=+%28-1%2F3%29%2A1%5E2+%2B+%282%2F3%29%2A1+%2B+8%2F3+\"
\n" ); document.write( "\"+3+=+9%2F3+\"
\n" ); document.write( "\"+3+=+3+\"
\n" ); document.write( "————————
\n" ); document.write( "( -2, 0 )
\n" ); document.write( "\"+0+=+%28-1%2F3%29%2A%28-2%29%5E2+%2B+%282%2F3%29%2A%28-2%29+%2B+8%2F3+\"
\n" ); document.write( "\"+0+=+-4%2F3+-4%2F3+%2B+8%2F3+\"
\n" ); document.write( "\"+0+=+0+\"
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "
\n" );