I began class explaining what a quadratic was. I showed some examples – some in vertex form (which the kids were used to) and some in standard form just to show them that the highest exponent of x was 2. There is a section on polynomials later so I didn’t go into standard form too much.
I then spent awhile on the Venn diagram of real numbers that appears at the bottom of page 499. Strangely(?!), the students seemed to like this exercise.
Next, I explained how quadratic equations could have 0, 1, or 2 solutions. I did so by showing what (x + 1)² = 10 would look like on a graph and then asked how we could change the “10″ so that we had just one or zero roots.
I then spent some time explaining what what square roots were and how they “undo” squaring. Going back to simple equations such as x² = 9, I showed the students that there were two possible solutions, ±3. When solving quadratics in vertex form, I focused their attention on the fact that 6 ±√3 is actually two different numbers.
Once we had x = 6 ±√3 I wrote “(exact answers)” after it and then below that I wrote the approximate solutions and wrote “(approximate answers)” there. I know that students have a difficult time thinking that 6 +√3 is a simplified, exact answer – they’d rather find “one” number despite me trying to get them to think of “6 +√3″ as a single number. I think that will come with time.
By now the class period was near the end, so I gave them two quadratic equations to solve to take home.
