# Math Help - Sign Graphs

1. ## Sign Graphs

Can someone explain how to do sign graphs for inequalities?

Like (x-3)(x+4)>0

2. Hello, mm99!

Can someone explain how to do sign graphs for inequalities?

Like: . $(x-3)(x+4)\:>\:0$
Here's one way . . .

We have the graph of: . $y \:=\:(x-3)(x+4)\quad\Rightarrow\quad y \:=\:x^2+x-12$

This is an up-opening parabola.
We want to know when this graph is positive (above the x-axis).

Draw a sketch (or visualize it) . . .
The x-intercepts are $x = -4,\:3$
The graph is positive to the left and right of the intercepts.
Code:
                      |
*                |            *
|
*               |           *
*              |          *
- - * - - - - - - + - - - - * - -
-4 *           |       * 3
*       |   *
* |
|

Therefore: . $(-\infty,\:-4) \cup (3,\:\infty)$