1. Math 2: Unit 6 Day 3 How do we use curve fitting?
How do we interpolate and extrapolate values from a regression curve?

2. where the vertex is ( h, k) where p and q are the x-intercepts
Quadratic Functions we will be writing quadratic functions using vertex and intercept form
where the vertex is ( h, k)
where p and q are the x-intercepts
You will either be given the vertex and a point on the curve or the x-intercepts and a point on the curve. You will use that information to find a and then write the equation.

4. 2. vertex: (-2, -22) 3. vertex: (4, 1) point: (2, -18) point: (8, 17)
Write a quadratic function in vertex form whose graph has the given vertex and passes through the given point.
2. vertex: (-2, -22) 3. vertex: (4, 1)
point: (2, -18) point: (8, 17)

5. 4.

6. 5. x-intercepts: -3, 7 6. x-intercepts: 4, 6
Write a quadratic function in intercept form whose graph has the given x-intercepts and passes through the given point.
5. x-intercepts: -3, x-intercepts: 4, 6
point: (6, -9) point: (5, -2)

7. Curve fitting: Finding a line or curve that matches a set of data points
Types of curve fitting:
Linear Regression, a method for finding the equation of a line of best fit (previously discussed)
Quadratic Regression, which we will discuss today
Quadratic Regression:
the process of finding the best-fitting quadratic model for a set of data

8. To determine which equation is the best-fitting model, substitute in values and chose the equation that the most points lie close to.
Example: Determine the equation that best models the data. x 2 7 9 13 17 20 25 y 34 37 38 36 32 26 A. x 3 4 5 6 7 8 9 y 15 30 40 50 45 42 31 B.

9. Interpolation: Extrapolation:
used to make predictions within the domain of values of the independent variable
Use a linear or quadratic regression model to find interpolated values
Extrapolation:
the use of a regression curve to make predictions outside the domain of values of the independent variable
Often unreliable, so determine if feasible

10. Women’s Age and Muscle Mass A nutritionist randomly selected 10 women over the age of 40 and measured their muscle mass. The results are in the table below:
Example
Age 71 64 43 67 56 73 68 76 65 MM 82 91
100 87 78 80 84
Make a scatter plot and find a linear regression line to model the data.
Predict the muscle mass of
a 60 year old woman. 40 45 50 55 60 65 70 75 80 90
100
110
120

11. Speed vs. Fuel Efficiency For Trucks
Example
Speed (in mph)
Fuel Efficiency (in mpg) 55 18 60
17.5 65
16.6 70
14.9 75
13.9 80
13.0
Find the regression line for this set of data.
Interpolate the fuel efficiency that a truck going 68 mph.
Extrapolate the fuel efficiency of a truck going 85 mph.
Now, try to calculate the fuel efficiency at 160 mph.
Which result does not make sense and why?

12. Homework:
Unit 6 Day 3 Handout