Math Is Fun Forum

Faced with this quadratic I was tasked with finding the vertex and y-intercept: -3/2x^2-6x

I could just use the formula -b/2a but because I'm learning to fully understand rather than just memorize shortcuts, I take the long way.  Get rid of -3/2 by multiplying everything by -2/3 and left with: x^2+4x

I complete the square to get (x+2)^2-4 (half of 4 is 2, 2 squared is 4, subtract a 4 to maintain equality).. but this is wrong and I still don't know why it's wrong.  This gives me the vertex (-2,-4) but the correct vertex is (-2,6).  Where am I messing up?  The only way I can reach (-2,6) as an answer is if I had -2/3 on the other side of the equation in the first step, to end up with x^2+4x=-2/3.  Then multiply the lone -4 at the end by -3/2.. but isn't that not possible?  If the equation is set to equal zero and I multiply everything by -2/3 in the beginning, wouldn't I just be left with zero on the other side of the equation?

Hey.  I've always wanted to learn geometry by myself, but don't really know where to start.  Somebody mind helping me out a bit?  Books, websites, anything.

Thanks