Quadratic Regression

The last part of Unit 3 in Analytic Geometry is using quadratic regression to model real-life scenarios.  Here are a couple of links to something similar to what we are doing in class:

http://www.mesacc.edu/~scotz47781/mat120/notes/projectile_motion/projectile_motion.html

http://www.algebralab.org/Word/Word.aspx?file=Algebra_QuadraticRegression.xml



The test for Unit 3 is on Friday, 9/25.  It will focus on graphing quadratics and characteristics of parabolas.

9/23 Analytic Geometry Milestones Question of the Day

Wednesday, 9/23/2015

Find the zeros of the polynomial function: g(x) = x² + 8x – 20

AG QOTD - Tuesday, 9/22

Tuesday, 9/22

Match a - d with 1 - 4.

a. x = -1 b. x = -1 and x = 2/3 c. x = -½      and x = 3 d. x = -5   1. x2 + 2x + 1 =0  a  b  c  d   2. x2 + 10x + 25 = 0  a  b  c  d   3. 6x2 + 2x – 4 = 0  a  b  c  d   4. 8x2 – 20x – 12 = 0

Milestones QOTD - Monday, 9/21

Monday, 9/21/2015

A rectangle has a length of 6 feet.  The value of the area of the rectangle, in square feet, is an irrational number. Therefore, the number that represents the width of the rectangle must be —

     A)  a whole number

     B)  a rational number

     C)  an irrational number

     D)  a non-real complex number.

Square Root and the Tangent Line (cool name for a band...)

As AP Calculus was ending this morning, we were finding the equation of the tangent line to the square root curve at the point (1,1).  I graphed the tangent line and the square root function on the same coordinate plane and then zoomed in really close.  What we can notice is that as we zoom in closer and closer to (1,1), the difference between the curve and the tangent line becomes negligible.  This is one of the reasons we simplify things by saying the slope of the tangent line is the slope of the curve.

Check out the picture if you're interested.













PS: +5 on a quiz grade if you bring me a printed copy of the picture by Wednesday, 9/23.

PPS: Cambridge Cambridge Cambridge (https://en.wikipedia.org/wiki/Isaac_Newton)

Milestones Question of the Day

As long as people refer to it or indicate they are looking at this, I will post a Georgia Milestones Analytic Geometry Question of the Day on the blog.  Students can practice these questions and turn in their answers with work and explanations.  I'm going to shoot for putting a new one on everyday.  After at least ten Questions have been posted, students may turn in ten questions at a time to me.  If all ten are correct and there is work AND at least one sentence explaining why that choice is the correct answer, then students can trade in the ten correct Questions and replace their lowest homework or quiz grade with a 100.

Here's the first QOTD:

Friday, 9/18/2015

Use these functions to answer this question.

P(x) = x² – x – 6

Q(x) = x – 3

What is P(x) – Q(x)?

A) x² – 3

B) x² – 9

C) x² – 2x – 3

D) x² – 2x – 9

                                                                                                                                                                                                   Super Gigantic Bonus:  The walls are looking a little plain in the classroom and pretty much have the same stuff on them since the beginning of the semester. Time for an update.  Take a normal-sized sheet of poster board.  Using different colors and your special creative juices, bring in something related to one of the topics we have discussed thus far this semester.  For example, you could put the quadratic formula, or the difference of squares pattern, or Pascal's Triangle, or the definition of continuous, or some of the unit conversion stuff (those last two are for AP Calculus and Algebra I Support students).  Bring this in by Wednesday, 9/23, and I will give you 10 points on your lowest test (or a 100 for your lowest assignment in Algebra I Support).  See me, Mr. Lewis, for details.  One entry per student, void where prohibited.

The Latest in Analytic Geometry

Test # 2 is graded and will soon be posted in Power School.  Thanks for your patience.  There are so many ways to gain some partial credit that it takes a while to get an accurate grade on these kinds of assessments.

We started our study of Unit 3 on Friday, 9/11/2015.  Now that we have spent so much time working with quadratic functions algebraically and solving quadratic equations by completing the square, factoring, and using the Quadratic Formula, we are turning our attention to graphing quadratic functions.

We have learned that the graph of a quadratic function is called a parabola, and the important features of parabolas are the vertex and the axis of symmetry.

Below are copies of some of the handouts we have looked at in class as well as links to videos, lessons, practice, and other cool web resources for parabolas.

Graphic Organizer
https://drive.google.com/file/d/0B2XYF8oNHClQUGF1dVBBUkpQaDg/view?usp=sharing

Worksheets from Class
https://drive.google.com/file/d/0B2XYF8oNHClQZ0lBOE9tSF9mNzg/view?usp=sharing

https://drive.google.com/a/oconeeschools.org/file/d/0B2XYF8oNHClQV2NHTUc0T1ItMEE/view?usp=sharing

https://drive.google.com/a/oconeeschools.org/file/d/0B2XYF8oNHClQV3otWnJuZnJJWDA/view?usp=sharing

Cool Websites
https://www.khanacademy.org/math/algebra/quadratics/solving_graphing_quadratics/v/graphing-a-quadratic-function

http://www.purplemath.com/modules/grphquad.htm

https://www.youtube.com/watch?v=rnkk0rC9Gyo

http://www.mathwarehouse.com/quadratic/parabola/interactive-parabola.php

http://calculator.tutorvista.com/math/604/parabola-calculator.html

http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php

http://www.vonsteuben.org/ourpages/auto/2010/2/23/60868648/Graphing%20Parabolas%20Worksheet%202%20with%20Answer%20Key.pdf

http://www.regentsprep.org/regents/math/algebra/ac4/pracpar.htm



PS:
Please get one of these...  I don't care where you buy it from.  I don't care if you use big sister's old one.  I don't care what kind of TI you get (or other brand, but I really really really like Texas Instruments calculators).  I can't make you buy one.  But, if you don't have access to a calculator and you have been trying to borrow one of the rescued calculators I have to solve the arithmetic problems you have not been able to solve on your own, then please please please get ahold of one to use.  You will be glad!

Analytic Geometry Stuff

One of the challenges of the numerous changes to mathematics curriculum in the state of Georgia throughout this millennium is that textbook companies do not tend to make specific textbook editions for the classes that our high schools are teaching.  Thus, we have become accustomed, as teachers and students, to not having textbooks in the classroom.

However, this millennium has also seen an explosion in the amount of resources available to us via the internet (ask an adult to comment on the cutting-edge technology that appeared at the beginning of the Tom Hanks movie, "You Got Mail").

To address this two things, I will try to keep up a semi-decent list of websites with tutoring guides, videos, and extra practice (worksheets, interactive problems, games) that might help students and friends and family members explore the mathematics we are learning in class.

You will have to communicate to me if this is helpful in any way.


PS: I have always liked Purplemath and Khan Academy.  Lots of great videos are on You Tube, of course.

Solving Quadratic Equations

http://www.purplemath.com/modules/solvquad.htm

http://www.wikihow.com/Solve-Quadratic-Equations

http://www.regentsprep.org/regents/math/algtrig/ate3/quadcompletesquare.htm

http://www.mathportal.org/calculators/solving-equations/quadratic-equation-solver.php   ---  Pretty Cool!

Analytic Geometry Quiz # 4

Wednesday, 9/2, is Quiz Day in Analytic Geometry.  Here are some problems for those who want some more practice on factoring, solving equations with factoring, and solving equations with completing the square.