document.write( "Question 30642: I need to know the vertex and how to graph it. Thank you.
\n" ); document.write( "y=-2(x-3)(x+1) \n" ); document.write( "

Algebra.Com's Answer #17380 by Fermat(136) $\"\"$ $\"About$

You can put this solution on YOUR website!
A parabola which has its vertex at the point (a,b) can be written as,
\n" ); document.write( "(y-b) = (x-a)²
\n" ); document.write( "or,
\n" ); document.write( "(y-b) = C(x-a)²
\n" ); document.write( "if it is scaled.
\n" ); document.write( "You have y=-2(x-3)(x+1), so convert it to the above form.
\n" ); document.write( "y=-2(x-3)(x+1)
\n" ); document.write( "expand it,
\n" ); document.write( "y = -2(x² - 2x - 3)
\n" ); document.write( "y = -2(x² - 2x + 1 - 4)
\n" ); document.write( "y = -2{(x - 1)² - 4}
\n" ); document.write( "y = -2(x-1)² + 8
\n" ); document.write( "(y-8) = -2(x-1)²
\n" ); document.write( "================
\n" ); document.write( "Here the parabola has a scaling factor, 2, which means it is slimmer, and it has a change of sign, the minus sign, hence it is upside down.
\n" ); document.write( "The vertex is at the point (a,b) = (1,8)
\n" ); document.write( "========================================
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-4%2C+4%2C+-4%2C+10%2C+-2%28x-1%29%5E2+%2B+8%29+\"$ \n" ); document.write( "

\n" );