4.3 Modeling_1.1.notebook
October 19, 2011
4.3 Modeling With Quadratic Functions
You can write a quadratic function in standard form using any three points on the graph.
7. Write an equation in standard form of the parabola passing through the points (1, ­ 2), (2, ­ 2) and (3, ­ 4).
Substitute each (x, y) into y = ax2 + bx + c to write a system of equations.
1
4.3 Modeling_1.1.notebook
October 19, 2011
2
4.3 Modeling_1.1.notebook
October 19, 2011
3
4.3 Modeling_1.1.notebook
October 19, 2011
Quadratic Regression
Staring Michael Jordan
4
4.3 Modeling_1.1.notebook
October 19, 2011
Write a Quadratic Model of an equation of M.J. basket ball path. If the center of the hoop is at (12, 10), will the ball go through the hoop?
5
4.3 Modeling_1.1.notebook
October 19, 2011
Quadratic Regression
An equation that best models data that follows a quadratic pattern.
**Calculator Steps are the same as for Best-Fitting
Lines except for what type regression you choose!!
The following table shows the operating costs of a small business from 2000
to 2005. Assume that t is the number of years since 2000 and C is the cost in
thousands of dollars.
a) Use a graphing calculator to find the best-fitting quadratic model for the data.
1. Go to STAT
2. EDIT
3. Enter the data into L1 and L2
4. Go to STAT
5. ARROW Right to CALC
6. ARROW Down to #5 QuadReg
7. In Home screen you should now have QuadReg
8. Go to VARS, over to YVars, hit ENTER for Y1
b) Using the model, how much are the operating costs in 2008?
6
4.3 Modeling_1.1.notebook
October 19, 2011
The following table shos the number of scrap parts P produced by a large
manufacturing company from 1996 to 2004. Quality control is working to
eliminate the production of scrap. Assume that t is the number of years since
1996 and P is measured in thousands.
a) Use a graphing calculator to find the best-fitting quadratic model for the data.
b) What will the number of scrap parts be in 2005?
c) Using the graphing calculator model, in what year will the scrap parts theoretically be zero?
7
4.3 Modeling_1.1.notebook
October 19, 2011
The following table shows the number of
people (in thousands) that were unemployed
in Australia from 1990 to 1995. Assume
that t is the number of years since 1990.
a)
Make a scatterplot of the data on your calculator. Sketch it.
b)
Use your calculator to find the best fitting quadratic model for the data. Round
to the nearest hundredth.
c)
Find the maximum percentage for the data. In what year did the maximum occur?
8
4.3 Modeling_1.1.notebook
October 19, 2011
The table shows the percentage of eligible voters
that participated in presidential elections from
1964 to 1992. Assume that t is the number of
years since 1964.
a)
Make a scatterplot of the data on your calculator. Sketch it.
b)
data.
Use your calculator to find the best fitting quadratic model for the
Round to the nearest hundredth.
c)
Find the maximum percentage for the data. In what year did the
maximum occur?
9
4.3 Modeling_1.1.notebook
October 19, 2011
HW p. 212; 9,15­21 odd, 24­26
10