( ) f x x 

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Algebra 2
Notes – Lesson 5.3
[Type text]
f ( x)  x 2
The “Parent” Function of the Quadratic:
5
We can transform the quadratic
the same way we did with the
absolute value function.
4
3
2
1
“VERTEX FORM”:
f(x) = a(x –h)2 + k
-5 -4 -3 -2 -1
1
2
3
4
5
-1
-2
-3
a, h, and k do the
same things as before
-4
-5
Notice how the graph increases. Up 1 over 1. Up 3 over 1. Up 5 over 1.
Describe, in order, the sequence of transformations of each
function and then graph the function by hand.
2
1) f ( x)  2  x   4 2) f ( x)  1  x  2 2  5 3) f ( x)   1  x  12  2
3
2
5
5
5
4
4
4
3
3
3
2
2
2
1
1
1
-5 -4 -3 -2 -1
1
2
3
4
5
-5 -4 -3 -2 -1
1
2
3
4
5
-5 -4 -3 -2 -1
1
-1
-1
-1
-2
-2
-2
-3
-3
-3
-4
-4
-4
-5
-5
-5
2
3
4
5
Algebra 2
Notes – Lesson 5.3
[Type text]
Write a function for the graph below.
1. How is the graph
translated?
__________________
8
6
4
2. Use the translation
to write an equation:
__________________
2
-8
-6
-4
-2
2
4
6
8
-2
3. Find a value for a:
-4
-6
-8
Write a function for the graph below.
1. How is the graph
translated?
__________________
8
6
4
2. Use the translation
to write an equation:
__________________
3. Find a value for a:
2
-8
-6
-4
-2
2
-2
-4
-6
-8
4
6
8
Algebra 2
Notes – Lesson 5.3
[Type text]
Write a function for the graph below.
1. How is the graph
translated?
__________________
8
6
4
2. Use the translation
to write an equation:
__________________
3. Find a value for a:
2
-8
-6
-4
-2
2
-2
-4
-6
-8
4
6
8
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