Today’s topic is quadratic inequalities and comparing three different models (linear, exponential, and quadratic).
Like other inequalities we have learned, we want to be able to graph a quadratic inequality. Three steps will get you there:
- Graph the quadratic equation. If the inequality has an equal sign in it, use solid line. Otherwise use dashed line.
- Pick a point that is not on the graph and test it with the original inequality.
- Shade the solution area with the test result from Step 2. If the test result is true, the point is in the solution region, shade the region that contains the point. Otherwise, shade the other region.
So far we have learned three data models that can be used to express the relationships for a set of points: linear, exponential, and quadratic.
For linear model, the delta of two consecutive values should be constant. That is, for y = mx + b, y(x+1) – y(x) = m.
For exponential model y = C(1+/-r)^t, we know the ratio of two consecutive values should be contact. That is, y(t+1)/y(t) = 1+/-r.
If neither linear nor exponential relationship can be established, you can try quadratic model.
For homework, visit the following link:
http://blog.newtonchineseschool.org/wangweidong/files/2011/12/Math7_Fall_HW_L12.pdf
We don’t have school for the following two weeks and I will see you on 1/8/2012. Have a wonderful holidays.
