1. How do we solve quadratic inequalities?
Do Now: What is the difference between an equation and an inequality?

2. What are we trying to find when we solve inequalities?
We are trying to find the values of x that make the inequality true.
If we are trying to solve the inequality x2-x-6<0, then we want the values of x that would make y negative in the equation y=x2-x-6
We can look at the graph and see that this is true when -2<x<3

3. But how can we solve it algebraically?
First we want to factor.
(x-3)(x+2)<0
Next we solve for values of x that make the expression equal zero
x=3, x=-2
Now we put this on a number line

4. x2-x-6<0 -2 3
Since the inequality is simply less than zero, then we use an open circle to mark the points.
Note: If the inequality was less than or equal to zero, the the circle would be solid
Now, we pick a value in each section; x<-2, -2<x<3, 3<x and plug it into the inequality.

5. x2-x-6<0 - (-3-3)(-3+2)=(-6)(-1)=6 (0-3)(0+2)=(-3)(2)=-6-2 3 - + +
(-3-3)(-3+2)=(-6)(-1)=6
(0-3)(0+2)=(-3)(2)=-6
(4-3)(4+2)=(1)(6)=6
Finally, we express our answer in one of two ways:
Symbolically: -2<x<3
Graphically: Shade in the correct part of the number line

6. Example Given: x2-2x-20>4 Find the solution set.
Graph the solution set on a number line.

7. Summary/HW
If the problem is a quadratic, is there always a set pattern of positives and negatives?
HW pg 101, 1-16 even