What are the transformations from an original function to and to ?
Write an equation for and for using the transformations.
How does this equation compare to vertex form of a parabola? What features do you see in this form?
13.3
Activity
Your teacher will assign one of these equations to your group:
Rewrite your equation in vertex form by completing the square.
Identify the transformations from the equation to your equation.
Before graphing, identify the vertex and -intercept.
Graph your equation.
Student Lesson Summary
When we have an equation for a parabola in vertex form, we can see the transformations from an original function without graphing. Here is an example:
The graph of has been shifted left 6, stretched vertically by a factor of 4, and shifted down 7. This makes sense because the original vertex is at , and the new vertex is at , so it has been shifted left 6 and down 7 as well.
We can also see the transformations from an equation that is not written in vertex form, but we will need to rewrite it first. Take a look at this equation: . Let's rewrite it in vertex form by completing the square:
Now we can see that the vertex is at . Using this equation, we can identify the transformations from : shift left 5, vertical stretch by a factor of , shift down 6.
For any equation of a parabola in vertex form , we can identify the transformations: horizontal translation by , vertical stretch by a factor of , reflection over the -axis if , and vertical translation by .
