Positive - negative quadratic - Vertex

positive quadratic y = x2	negative quadratic y = - x2
If the coefficient of x2 is positive the curve looks like the mouth of a smiling child. The vertex (0,0) is down.	If the coefficient of x2 is negative the curve looks like the mouth of a joyless child. The vertex (0,0) is up.

Source: The purplemath

The meaning of a in a quadratic

The general form of a quadratic is:

y = ax² + bx + c. 

For graphing, the leading coefficient "a" indicates how "fat" or how "skinny" the parabola will be.

For | a | > 1 (such as a = 3 or a = –4), the parabola will be "skinny", because it grows more quickly (three times as fast or four times as fast, respectively (in the case of our sample values of a). 

For | a | < 1 (such as a = ¹/₃ or a = ^–1/₄ ), the parabola will be "fat", because it grows more slowly (one-third as fast or one-fourth as fast, respectively (in the case of our sample values of a). 

Also, if a is negative, then the parabola is upside-down.

You can see these trends when you look at how the curve y = ax² moves as "a" changes.

Click on the adjacent image (graph) -->

Source: The purplemath