Δευτέρα, 3 Ιανουαρίου 2011

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

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