5.3 Transforming Quadratic Functions
The “Parent” Function of the Quadratic:
f ( x)  x
2
5
We can transform the
quadratic the same way we
did with the absolute value
function.
f(x) = a(x
–h)2
+k
4
3
2
1
-5 -4 -3 -2 -1
1
2
3
4
5
-1
-2
a, h, and k do the
same things as before
-3
-4
-5
Notice how it 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
Down 4
Right 2
Left 1
Goes up twice as fast.
Down 5 for vertex.
½ as tall. Might be best to
plug in some points, then
use symmetry.
Up 2 for vertex
Reflected.
1/3 as tall.
Again, plug in some points
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
Write a function for the graph below.
Right 3
Up 4
8
6
So then
f(x) = a(x -3)2 + 4
Now you have to see whether
there is an ‘a’ or not.
So pick an (x,y) point, plug in-8
and check.
I picked (2, 3)
3 = a(2 – 3)2 + 4
-1 = a(-1)2
So a = -1
4
2
-6
-4
-2
2
-2
-4
-6
-8
4
6
8
Write a function for the graph below.
8
Left 2
Down 2
So f(x) = a(x + 2)2 -2
6
4
Point (-1, 0)
2
0 = a( -1 + 2)2 – 2
2 = a(1)2
a=2
f(x) = 2(x +2)2 -2
-8
-6
-4
-2
2
-2
-4
-6
-8
4
6
8
Write a function for the graph below.
Left 4
Up 7
f(x) = a(x +4)2 +7
8
6
Point (-2, 5)
4
5 = a(-2 + 4)2 + 7
2
-2 = a(2)2
-8
-6
-4
-2
2
a = -2/4 = -1/2
-2
f(x) = -1/2(x + 4)2 + 7
-4
-6
-8
4
6
8
5.3 Problems to do:
Pg. 255 #13-31 odd, 42, 43, 45, 47, 51
This is an important section so make sure you
know what you are doing.
Tutoring every M, W, T after school San Juan.
Midterm Take home due Thursday morning.
Work together, but no freeloaders!
Fear is the main source of superstition, and one of
the main sources of cruelty. To conquer fear is the
beginning of wisdom.