Parent Function of the Quadratic

This lesson will walk you through translation and transformations of parent functions to get other graphs from a parent function

Throughout this you will be diving into the quadratic function specifically. The first thing that needs to be mentioned is that a parent function of is the most basic form. For the quadratic the parent function is y = x² making the function look like the following

Using Desmos you are going to explore the and answer the following questions:

Step 1:

Type in the parent function y = x²

1. Make a table and fill in some x and y values
2. Where does the function start?
3. How do y values increase?

Step 2: 

Make a new graph for the quadratic y = x² + 2

1. Make a table and fill in x and y values
2. Where does this function start? How does it differ from the parent function

Step 3:

Make the graph y = (x+2)²

1. Make a table and fill in x and y values
2. Where does this function start?  How does it differ from the previous functions

Step 4:

Make the graphs y = 2x² and y = ½ x²

1. Make a table and fill in the x and y values
2. Where do these functions start? How do they compare to the parent function
3. How do the y values increase for each? How do they compare to each other and the parent function 

Step 5:

Make the graph y = (2x)² and y = (½x)²

1. Make a table and fill in the x and y values
2. Where do these functions start? How do they compare to the parent function
3. How do the y values increase for each? How do they compare to one another and the parent function?

Watch the following videos to describe the translations and transformations you have just discovered:

Horizontal Shifts

Vertical Shifts

Horizontal/Vertical Stretch and Shrink

Now that you have explored a few different transformations and translation

You will now be tasked with taking the parent function y = x² and use the knowledge you just discovered to move the graph to the left 7 units, up 6 units, a horizontal stretch of 3 times, and a vertical stretch of 2 

Describe your choices for what you did to the parent function 

You have now explored transformations and translations of parent functions and how you can use them to interpret and create new graphs from the original 

Indiana Standards:

AII.MFD.4 Explore the effects of function transformations using graphing technology. Explain the effects of transformations of functions such as f(x)+k, kf(x), f(kx),or f(x+k) for different functions and values of k.