## Constructing Linear, Quadratic, and Exponential Models of Data

#### Aligned To Common Core Standard:

**High School** - HSF-LE.A.2

Constructing Linear, Quadratic, and Exponential Models of Data -
Linear, quadratic, and exponential functions have independent value in the field of mathematics. Each of these models have different equations, let us discuss each of them differently.
**Linear Model** - The linear model should have an equation with the format y=mx+b, where m is the slope, while b is the y-intercept. For this model, we will take m and b as 1 each. They make a straight line if graphed.
(x, y) = (0, 1), (2, 3), (3, 4).
**Quadratic Model** - The quadratic model should have an equation with the format y= [ax]^{2}. Let us take a = 2 for different values of x. They make a parabola if graphed.
(x, y) = (0, 0), (1, 2) , (2, 8)
**Exponential Model** - Exponential Model should have an equation with the format of y=a^{x}. Let us take a = 4 for different values of x. The graph goes steeper with an increase in value.
(x, y) = (0, 1), (1, 4), (2, 64) These worksheets and lessons teach students how to create models of data in various formats.

### Printable Worksheets And Lessons

- Function It All
Up Step-by-step Lesson - You are given a table and asked to
write a linear, quadratic, or exponential function for it.

- Guided Lesson
- We build on the lesson and now we introduce some negative numbers
too.

- Guided Lesson
Explanation - The second one drags out a bit, but it makes sense
in the end.

- Practice Worksheet
- This page took two hours for one students of a teacher that wrote
in. You might want to do this over several days.

- Matching Worksheet
- I give you one of each form to find. You can reverse engineer
it, when using this type of worksheet.

#### Homework Sheets

Modeling data is not always a simple task. Think before attempting these questions.

- Homework 1 - The pattern of the y-values lets us know if the function is linear, quadratic, or exponential.
- Homework 2 - This allows us to compare each y value directly.
- Homework 3 - If the first difference between successive y-values is equal, this will be a linear function. If the second differences between the successive y-values are equal, the function is quadratic .

#### Practice Worksheets

Model all of the data in three different formats.

- Practice 1 - For each problem, write a:
a) linear (y = mx + b),
b) quadratic (y = ax
^{2}+ bx + c) or c) exponential (y = a(b)^{x}) function that models the data. - Practice 2 - Look at this table and write a linear (y = mx + b),
Quadratic (y = ax
^{2}bx + c), or exponential (y = a(b)^{x}) function that models the data. - Practice 3 - Since the x-values are consecutive and straight forward, it makes it much easier.

#### Math Skill Quizzes

Yet more modeling for you. This is a very lucrative skill to have in the real world.