Download Slide 1 - MrWaddell.net

Warmup Alg 2
19 Apr 2012
Agenda
• Don't forget about resources on
mrwaddell.net
• Section 9.2: Parabolas again!
• Non-Zero Vertex
• Completing the Square with Parabolas
Go over assignment from last
class period
Section 9.2: Graphing a Parabola
with a non-zero vertex
Vocabulary
Parabola
A function with a SINGLE
“squared” term
Axis of Symmetry
Focus
Focus
Directorix
Distances are
the same!
Vertex
Vertex
Directorix
Axis of symmetry
Non-Zero Standard equation
Standard Form
Vertical
Vertex Focus
(x - h)2 = 4p(y - k) (h, k) (h, k + p)
Horizontal (y - k)2 = 4p(x - h)
(h, k)
(h + p, k)
Directrix
y=k-p
x=h-p
Every point on a parabola is the same distance from the
focus as from the directrix
What it looks like
(x -
2
h)
= 4p(y - k)
What it looks like
(y - k)2 = 4p(x - h)
Graphing
(y - 3)2 = 16(x + 2)
1
(y
4∙4
Divide by 12 &
find “p”
- 3)2 = (x + 2) So, p = 3
Vertex is (-2, 3)
Focus is (-2+4, 3)
Why?
Why?
Directrix is x = -2 – 4 Why?
or x = -6
Vertex is (-2, 3)
Focus is (2, 3)
Directrix is x = -6
Graphing
(x +
1
(x
4∙5
2
4)
= 20(y + 2)
Divide by 20 &
find “p”
+ 4)2 = (y + 2) So, p = 5
Vertex is (-4, -2)
Focus is (-4, -2+5)
Why?
Why?
Directrix is y = -2 – 5 Why?
or y = -7
Graphing
Vertex is (-4, -2)
Focus is (-4, 3)
Directrix is y = -7
Simplest form
All the equation does is translate the graph.
Left or right is the number next to the “x”
Up or down is the number next to the “y”
But the sign changes! Keep it simple.
Completing the square
y2 – 10y + 5x + 57 = 0
We need to turn this into the standard form!
Recall from back in Chapter 4, the method
we used called Completing the Square.
Patterns in the “Genius Way”
x2 + 6x + 9
x2 + 8x + 16
x2 + 10x + 25
x2 - 14x + 49
x2 - 20x + 100
___
x2 - 16x + 64
___
x2 + bx + (b/2)
___ 2
(x+3)2
(x+4)2
(x+5)2
(x-7)2
(x-__)
10 2
(x-__)
8 2
(x+__
b/2)2
x2 + 7x + 49/4
___
(x+__)
7/2 2
Completing the square
y2 – 10y - 5x + 55 = 0
We take the “-10” (because the y is
squared), divide by 2, and square the
answer.
-10/2 = -5
(-5)2 = 25
Completing the square
y2 -10y -5x +55 = 0
+5x – 55
Our genius numbers
are -5 and 25
+5x - 55 Move stuff
y2 -10y +25 = 5x - 55 +25 Use the 25 to both
y2 -10y +25 = 5x - 30
Now we can factor
(y - 5)2 = 5(x – 6)
p = 5/4 (why?)
Vertex is (6, 5)
Focus is (6+5/4, 5)
Directrix is x = 6 - 5/4
You Try!
y2 +8y -3x + 22 = 0
+3x – 22
Our genius numbers
are 4 and 16
+3x - 22 Move stuff
y2 +8y +16 = 3x -22 +16 Use the 16 to both
y2 +8y +16 = 3x - 6
Now we can factor
(y +4)2 = 3(x – 2)
p = 3/4 (why?)
Vertex is (-4, 2)
Focus is (-4+3/4, 2)
Directrix is x = 6 - 3/4
You Try – Last one!
Our genius numbers
are 6 and 36
x2 +12x +8y -20 = 0
-8y +20
-8y +20 Move stuff
x2 +12x +36 = -8y +20 +36 Use the 36 to both
x2 +12x +36 = -8y + 56
Now we can factor
(x +6)2 = -8(y – 7)
p = -2 (why?)
Vertex is (-6, +7)
Focus is (-6, +7-2)
Directrix is x = 7 - -2
Assignment
Section 9.2:
Handout