Download - Warmup Alg 2 19 Apr 2012
Warmup Alg 2 19 Apr 2012
Agenda• Don't forget about resources on
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• 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
Focus
Directorix
Vertex
Axis of symmetry
A function with a SINGLE “squared” term
Focus
Directorix
Vertex
Axis of Symmetry
Distances are the same!
Non-Zero Standard equation
Standard Form Vertex Focus Directrix
Vertical (x - h)2 = 4p(y - k) (h, k) (h, k + p) y = k - p
Horizontal (y - k)2 = 4p(x - h) (h, k) (h + p, k) x = h - p
Every point on a parabola is the same distance from the focus as from the directrix
What it looks like
(x - h)2 = 4p(y - k)
What it looks like
(y - k)2 = 4p(x - h)
Graphing
(y - 3)2 = 16(x + 2) Divide by 12 & find “p”
(y - 3)2 = (x + 2) So, p = 3
Vertex is (-2, 3)
Focus is (-2+4, 3)
Why?
Why?
Directrix is x = -2 – 4or x = -6
Why?
Vertex is (-2, 3)
Focus is (2, 3)
Directrix is x = -6
Graphing
Divide by 20 & find “p”
(x + 4)2 = (y + 2) So, p = 5
Vertex is (-4, -2)
Focus is (-4, -2+5)
Why?
Why?
Directrix is y = -2 – 5or y = -7
Why?
(x + 4)2 = 20(y + 2)
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
(x+3)2
(x+4)2
(x+5)2
(x-7)2 x2 - 14x + 49
x2 - 20x + ___ (x-__)2 10 100
x2 - 16x + ___ (x-__)2 8 64
x2 + bx + ___ (x+__ )2 b/2 (b/2)2
x2 + 7x + ___ (x+__)2 7/2 49/4
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 = 0Our genius numbers are -5 and 25
+5x – 55 +5x - 55 Move stuff
y2 -10y = 5x - 55 Use the 25 to both +25 +25
y2 -10y +25 = 5x - 30 Now we can factor
(y - 5)2 = 5(x – 6)
Vertex is (6, 5)
Focus is (6+5/4, 5)Directrix is x = 6 - 5/4
p = 5/4 (why?)
You Try!
y2 +8y -3x + 22 = 0Our genius numbers are 4 and 16
+3x – 22 +3x - 22 Move stuff
y2 +8y = 3x -22 Use the 16 to both+16 +16
y2 +8y +16 = 3x - 6 Now we can factor
(y +4)2 = 3(x – 2)
Vertex is (-4, 2)
Focus is (-4+3/4, 2)Directrix is x = 6 - 3/4
p = 3/4 (why?)
You Try – Last one!
x2 +12x +8y -20 = 0Our genius numbers are 6 and 36
-8y +20 -8y +20 Move stuff
x2 +12x = -8y +20 Use the 36 to both+36 +36
x2 +12x +36 = -8y + 56 Now we can factor
(x +6)2 = -8(y – 7)
Vertex is (-6, +7)
Focus is (-6, +7-2)Directrix is x = 7 - -2
p = -2 (why?)
Assignment
Section 9.2: Handout