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

#### 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=ax. 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 = ax2 + 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 = ax2 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.

• Quiz 1 - You can test for exponential functions by finding the ratios between successive y-values. If the ratios are equal, it is exponential.
• Quiz 2 - Find the first and second differences in the table.
• Quiz 3 - If the second differences are not all equal, the function can't be quadratic.