document.write( "Question 605216: write an quadratic function that has a vertex(-2,-4) and passes through the points (0,0). \n" ); document.write( "

Algebra.Com's Answer #381580 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
When the equation is of the form
\n" ); document.write( " $\"+ax%5E2+%2B+bx+%2B+c+\"$ , the vertex is at
\n" ); document.write( " $\"+x%5Bv%5D+=+-b%2F%282a%29+\"$
\n" ); document.write( "given:
\n" ); document.write( " $\"+-b%2F%282a%29+=+-2+\"$
\n" ); document.write( " $\"+-b+=+-4a+\"$
\n" ); document.write( " $\"+b+=+4a+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+y%5Bv%5D+=+-4+\"$
\n" ); document.write( " $\"+-4+=+a%2A%28-2%29%5E2+%2B+b%2A%28-2%29+%2B+c+\"$
\n" ); document.write( " $\"+-4+=+4a+-+2b+%2B+c+\"$
\n" ); document.write( "and, from above,
\n" ); document.write( " $\"+-4+=+4a+-+2%2A%284a%29+%2B+c+\"$
\n" ); document.write( " $\"+-4+=+4a+-+8a+%2B+c+\"$
\n" ); document.write( " $\"+c+=+4a+-+4+\"$
\n" ); document.write( "So far, I have
\n" ); document.write( " $\"+y+=+ax%5E2+%2B+%284a%29%2Ax+%2B+4a+-+4+\"$
\n" ); document.write( "and this must go through (0,0), so
\n" ); document.write( " $\"+0+=+a%2A0+%2B+%284a%29%2A0+%2B+4a+-+4+\"$
\n" ); document.write( " $\"+4a+=+4+\"$
\n" ); document.write( " $\"+a+=+1+\"$
\n" ); document.write( " $\"+b+=+4a+\"$
\n" ); document.write( " $\"+b+=+4%2A1+\"$
\n" ); document.write( " $\"+b+=+4+\"$
\n" ); document.write( " $\"+c+=+4a+-+4+\"$
\n" ); document.write( " $\"+c+=+4%2A1+-+4+\"$
\n" ); document.write( " $\"+c+=+0+\"$
\n" ); document.write( "So, the equation is:
\n" ); document.write( " $\"+y+=+x%5E2+%2B+4x+\"$
\n" ); document.write( "here's a plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-6%2C+10%2C+-6%2C+10%2C+x%5E2+%2B+4x+%29+\"$
\n" ); document.write( " \n" ); document.write( "

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