Excuse me , I had a strange question :). In algebraic geometry, a quadratic expression can be written as the product of two different linear equations, for example: y = x² + 3x - 4 can be factored as y = (x+4)(x-1). (x+4) and (x-1) are two parallel line and do not intersect.
geometrically, I don't understand why their product is a quadratic expression. I can understand algebraically that the multiplication of their terms forms a quadratic expression, but I don't understand it geometrically. I would appreciate it if you could guide me.