document.write( "Question 287759: find the quadratic function that indicate vertex (5,12) and passes through points (7,15)? \n" ); document.write( "

Algebra.Com's Answer #208532 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Put the equation in the form
\n" ); document.write( " $\"y+=+ax%5E2+%2B+bx+%2B+c\"$
\n" ); document.write( "The x-coordinate of the vertex is at $\"-b%2F%282a%29\"$
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"-b%2F%282a%29+=+5\"$
\n" ); document.write( "(2) $\"12+=+a%2A5%5E2+%2B+b%2A5+%2B+c\"$
\n" ); document.write( "(3) $\"15+=+a%2A7%5E2+%2B+b%2A7+%2B+c\"$
\n" ); document.write( "This is 3 equations and 3 unknowns, so it's solvable
\n" ); document.write( "(1) $\"b+=+-10a\"$
\n" ); document.write( "Subtract (2) from (3)
\n" ); document.write( "(3) $\"15+=+49a+%2B+7b+%2B+c\"$
\n" ); document.write( "(2) $\"-12+=+-25a++-+5b+-+c\"$
\n" ); document.write( " $\"3+=+24a+%2B+2b\"$
\n" ); document.write( "And, by substitution,
\n" ); document.write( " $\"3+=+24a+%2B+2%2A%28-10a%29\"$
\n" ); document.write( " $\"3+=+24a+-+20a\"$
\n" ); document.write( " $\"4a+=+3\"$
\n" ); document.write( " $\"a+=+3%2F4\"$
\n" ); document.write( "and
\n" ); document.write( " $\"b+=+-10a\"$
\n" ); document.write( " $\"b+=+-30%2F4\"$
\n" ); document.write( " $\"b+=+-15%2F2\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"15+=+49a+%2B+7b+%2B+c\"$
\n" ); document.write( " $\"15+=+49%2A%283%2F4%29+%2B+7%2A%28-15%2F2%29+%2B+c\"$
\n" ); document.write( " $\"15+=+147%2F4+-+105%2F2+%2B+c\"$
\n" ); document.write( "I made a mistake somewhere after this,
\n" ); document.write( "hope I gave you a good start \n" ); document.write( "

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