3.3 Quadratic Inequalities
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we can solve: 3x + 2 > 5 (linear inequality)
how about x2 - 4 > 0 ?
(quadratic inequality)
need to use a completely different method
just look at the graph of f(x) = x2 - 4:

y



   





x




Note:
 x2 - 4 > 0 (above the x-axis) for x < -2 or x > 2
 so the solution to the inequality is: (-, -2)  (2, )
You can do this without using your graphing calculator
(please don’t use it!); use the graphical method, p. 207.
Here’s how to solve x2 - 4 > 0 :
1. Determine if the parabola opens up or down:
the leading coefficient is > 0  up
the leading coefficient is < 0  down
2. Determine its x-intercepts: solve x2 - 4 = 0
3. Make a rough graph (very rough - only needs to show
the parabola passing through the intercepts and whether
the parabola opens up or down) – this step is required in
order to support your answer!
4. Write your answer
3.3-1