The line y = k intersects the graph of y = 3x2 in points A and B. Points C and D are on the x-axis and ABCD is a rectangle. If the area of ABCD = 128/9, what is the value of k? Calculators not allowed. Show your method clearly!
The above question is designed for students in their second year of algebra or precalculus. It can also be used for practice for the Algebra 2 questions on the SAT, although it is somewhat above that level. Many students, including the more advanced, tend to struggle with problems like these because they don't have that much experience with coordinate geometry questions. These types of problems are critical for their later development. Once the students have done a few of these they do not find them so formidable. A useful pedagogical tool is to let them try it, review the method clearly, then erase the board and call on students to recall each step. Tell them you will do this, encouraging them to take good notes and pay careful attention! When using it on an assessment, make it a bonus the first time, then make it count. Some of my readers may recall a similar parabola problem a few months ago.