Yesterday we learned about Basic Transformations and how to graph functions.
Graphing any quadratic function is moving (translating), flipping (reflecting), and stretching the base of the graph.
The base of the graph is y=x²
In the function f(x)=a(x-h)²+k, we learned that the variables (a, h and k) are an important part of graphing.
In the first function we have f(x)= 2(x+3)² -1. These numbers have changed the way the transformation was graphed.The values H and K will tell us if the graph must be moved left or right or up and down but I'll get into that later.
The number 2 tells us if the graph will be wider, narrower or the normal u-shape.
*Remember:
If the a-value is < 1, it is narrower
If the a-value is > 1, it is wider
If the a-value is = 1, it is the normal u-shape.
We used the following tables to represent the ordered pairs on a graph.
These tables show how the function y=x² has changed to y=2(x+3)²-1.
The first table represents the normal function.
In the second table, the y-values were multiplied by 2 but the x-values had stayed the same.
In the third table, 1 was subtracted from the y-values and the x-values still stayed the same.
In the fourth table, 3 was subtracted from the x-values and the y-values stayed the same.
We also learned about how to graph horizontal and vertical translations.
*Note: Read h values as opposite and k values as is!
Vertical translation, given f(x), k > 0:
y=f(x) + k ----> This tells us that the graph will move k-units up because k is positive.
y=f(x) - k -----> This tells us that the graph will move k-units down because k is negative.
Horizontal translation, given f(x), h > 0:
y=f(x - h) -----> This tells us that the function must shift h-units to the right.
y=f(x + h) ----> This tells us that the function must shift h-units the the left.
Using the graph of f(x), we had to graph f(x)+1.
How we graphed f(x)+1 was by adding 1 the the y-values.
* y = k
k = +1
And that's pretty much it.
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