As a middle school math teacher, I spend a lot of time slogging through review material. Our current textbooks don't challenge the students very much; much of what they see is simply a repeat of what they studied last year with a few new vocabulary thrown in.

So when I get to introduce a lesson on a topic that is a certain distance from what the students have seen before, it's always an exciting day. Today in seventh grade we dove into the graphs of quadratic functions--at a very basic level, granted, but the students always step over the bounds of the textbook and ask great questions:

- Does the parabola ever bend back in on itself?
- How can the slope of a curve increase but never reach straight up-and-down?
- Is it a quadratic function if it has powers of 0? How about -2?
- Will the scales of the axes be the same for all quadratic functions?
- What should I do if the y-intercept of the parabola is inconveniently large?
- Can I put a break in the axes of a coordinate plane?
- Is an expression still a polynomial if it has higher powers of the variable than 2?
- What do the graphs of higher-order polynomials look like?
- What does the function for this (fourth quadrant) parabola look like?

## 1 Comments:

alright...

i don't really get what are these questions talking about.

but they do seem intelligent.

lol

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