Quadratic Data (Algebra One)

http://www.ats.ucla.edu/stat/mult_pkg/faq/general/y6.png

This was the last topic we had time for in our Algebra One quadratics unit. We did not manage to get to the discriminant anywhere, something I wanted to do but as we sketched out the end of the year I realized we just wouldn't have time.

We also didn't have time for a performance task, or a unit test. We just did quizzes and one big quest halfway through. And we had the final exam to prepare for.

Here is my lesson plan for introducing quadratic data:

Working with Data – Quadratic Functions

Objectives

Students will be able to

·         Apply quadratic regression analysis to data sets and analyze the data with the resulting equations.  They will do interpolation, extrapolation, find minimum or maximum values and intercepts – relating all to the problem situation. (same objectives over the entire lesson)

What will students do to learn this?

First Day:

·         Start class with quiz on vertex form

·         Activity  HIV data. Discuss – emphasis is on visualizing quadratic data and what it means in terms of a trend, creating a graph (both by hand & on calculator) and understanding the significance of the maximum value.

·         ISN insert – finding characteristics on the calculator

·         Considering a visual parabola:

 measuring a tunnel example (on ppt) – with provided scenario students will

a)    Input the data into their graphing calculator and draw a rough sketch of their graph (label axes)

b)    Write a quadratic function equation f(x) for the data (use STAT CALC #5).

c)    What is the R² value and what does this tell you about the fit of the function to the data?

d)    What is the vertex of this graph? What does it represent in this problem situation?

e)    Interpolation – Calculate f(4) and explain what your result means with respect to the problem situation.

f)     Extrapolation – Calculate f(10)  and explain what your result means with respect to the problem situation.

g)    What is the y-intercept of this graph and what does it represent?

h)    What is the positive x-intercept of this graph? What does it represent?

 Second day - work with data sets 

Here is the ISN insert

next year I want to do a "right hand reflect" example opposite this. 

And this folder has all my ISN templates for this unit (8 blog posts worth! I'll post this link on each blog). It's way easier to upload them all together.

Here are supportingmaterials I used for this topic.