## Precal Files: Quads and Polys

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:

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

Review graphing polys:

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!

1. 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.

• 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.

• Thanks!