Chapter 5 Section 3
Transforming Parabolas
Algebra 2 Notes
March 4, 2009
Warm-Ups
• A rock club’s profits from booking local bands
depends on the ticket price. Using past receipts,
the owners find that the profit can be modeled
by the function
1) What do t and P represent?
2) What is the maximum profit?
3) How much does the club have to sell the tickets
for in order to achieve the maximum profit?
Homework #33 Answers
8
22)
2
25)
6
4
-2
-4
Max Value = 6
28) $10; $13,500
29) 2 s; 64 ft
30) 1000 tires; $20
2
-5
-2
Min Value = 2
37) B
38) C
39) A
Challenge Problem
• The local park has 350 feet of fencing for a
rectangular dog park. What dimensions maximize
the area the dogs can play in? What is that area?
1. Write an expression for the perimeter in terms of x
(width) and y (length)
2. Write an expression for the area of the rectangle in
terms of x and y.
3. Solve your perimeter equation for y. Plug that into the
area equation and simplify.
4. Use this equation to find the dimensions (x and y) that
maximize the area.
5. Find the maximum area using these dimensions
f ( x)  x
The “Parent” Function of the Quadratic:
2
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
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
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
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
Homework #34
• Page 255 #1, 4, 9, 14, 16, 19, 25-27,
34, 42bcd, 47, 51
– Read Example 4 on page 255 to help you
with #27 and #34
– Remember: Tutoring M-Th in the Media
Center from 3:30-5:00
• 5 pts EC for every hour you go!!!
• Bring me a sheet signed by Mr. Sloop with the
date and the amount of time you were there!