1. Section 2.1: Linear and Quadratic Functions and Modeling
Do Now
1) Find the inverse of f(x) = 3x – 1
2+4x
2. f(f-1(x)) = f-1(f(x))

2. Identify polynomial functions.
A function with exponents greater than or equal to zero. Determine if the functions are polynomials. a) b) c)

3. Write equations for linear functions satisfying given conditions.
Determine the equation of the linear function with the given conditions.
A line that passes through (-1, 3) and (5, -9)
f(2)=1 and f(6)=9
A line with x-intercept of 3 and y-intercept of -2

4. Graph, analyze, and write equations of quadratic functions.
Quadratic equation in standard form: Quadratic equation in vertex form:
Determine the coordinates of the vertex and the equation of the axis of symmetry. a) b) c)

5. More with Quadratic Functions
Use the process of completing the square to rewrite each standard equation in vertex form. a) b) Now, determine the max or min value of each function. Where is each function increasing?

6. Write an equation for a quadratic function whose graph contains a vertex of (1, 3) and point (0,5).

7. Apply linear and quadratic models.
Using quadratic regression on the data in the table below, predict the year when the number of patent applications will reach 350,000. Let x = 0 stand for 1980, x = 1 for 1981, and so forth.
Year
Applications (thousands)
1980
113.0
1985
127.1
1990
176.7
1995
228.8
1996
211.6
1997
233.0
1998
261.4
1999
289.5

8. More Modeling
A group of female children were weighed. Their ages and weights are recorded in the table below.
View a scatter plot of the data.
Find the linear regression model.
Interpret the slope of the linear regression equation.
What is the correlation coefficient? Is this a good model?
Use the regression model to predict the weight of a 30-month old girl.
Age (months)
Weight (pounds) 19 22 21 23 24 25 27 28 29 31 34 32 38 43 39

9. Investigative Activity
Catarina and Tom want to buy a rug for a room that is 8 by 12 feet. They want to leave an even strip of flooring uncovered around the edges of the room. How wide a strip will they have if they buy a rug with an area of 12 square feet?
Help yourselves by drawing a diagram and coming up with expressions to represent the length and width of both the room and the rug. Then, use this information to develop an equation you can solve. Be sure to check answers to see which answer or answers are possible.