Ok, technically, “Quadrilaterals and Polynomials,” but doesn’t “Quads and Polys” sound more fun? Also, this is my second-to-last unit for my Precal Files so my goal of having them up before school starts may actually happen! (See more of the files and FAQs here).

So *most* of this *should* be a review for Precal students so we booked through quite a lot of it. Starting with a quick review of parabolas:

(file here, modified from unknown source)

Some homework for the chapter:

(file here)

Then we did a really cool NMSI activity about concavity. I added this to the end of it for a little derivative preview:

(file here)

Review graphing polys:

(file here)

And dividing polys:

And solving polys!

And solving polynomial/rational inequalities:

(file here) I did a factor-sign-row chart and we also did a mini-graph on some to determine the signs. If you’d like to see more about the factor-cool-way to do sign charts, here’s a showme video of me doing a quick explanation.

A pretty intense group-work day on these inequalities:

(file here) And then wham, bam, time for the study guide!

(file here) And if you’re superinterested (or want to use the study guide and not make a video yourself), here is the showme video key.

Only one more unit to go! Woot woot!

*Related*

## Andria K.

January 17, 2016 at 7:24 pm

Hi, I’m looking at your first NTM on the page in the graphing with vertex form section. Could you explain the modified t-chart? I’m just not understanding what’s going on there. Thanks.

## Meg Craig

January 23, 2016 at 8:44 am

Suppose you want to graph y = (x – 4)^2 + 5. I know the vertex is at (4, 5). In plain old everyday x^2, the vertex is at (0, 0) and we graph a t-chart of (-2, 4)(-1, 1)(0, 0)(1, 1)(2, 4). Well, now I can just pretend my new vertex at (4, 5) is playing the role of the origin, or (0, 0) and graph the t-chart points from the vertex–left 2 from 4 and up 4 from 5; left 1 and up 1 from (4, 5), etc.

Now, what if there is stretch factor, for example y = 3(x – 4)^2 + 5? I know that the 3 will stretch the y-values vertically, or in other words, multiply all the y-values by 3. So I can take the basic t-chart and multiply all the y-values by 3 to get (-2, 12)(-1, 3)(0, 0)(1, 3)(2, 12), which I will then graph from the vertex of (4, 5). In the third example, there is a stretch and flip factor of -2, so I multiplied all the y-values by -2.

You might want to scroll down on this post for my NTM on transforming all the parent functions for more examples.

## Andria K.

February 21, 2016 at 12:08 pm

Thanks!