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**SAT Multiple Choice Question(s)**

For the two intersecting lines above, which of the following must be true? I. II. III. I only II only I and II only II and III only I, II, and III

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**SAT Multiple Choice Question(s)**

For the two intersecting lines above, which of the following must be true? I. II. III. I only II only I and II only II and III only I, II, and III

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**1. Center: (1,2) vertices: (4,2),(-2,2),(1,4),(1,0) **

Answers to HW: 1. Center: (1,2) vertices: (4,2),(-2,2),(1,4),(1,0) foci: (3.2, 2),(-1.2, 2) 2. Center: (-3,2) vertices: (-7,2),(1,2),(-3,7),(-3,-3) foci: (-3,-1),(-3,5) 3. Standard Form: (x-5)2/48 + (y-5)2/64 = 1 Center: (5,5) foci: (5,9),(5,1) vertices: (5,13),(5,-3),(-1.9, 5),(11.9, 5) 4. Standard Form: (x+2)2/64 + (y-1)2/48 = 1 Center: (-2,1) foci: (-6,1),(2,1) vertices: (-10,1),(6,1),(-2, 7.9),(-2, -5.9)

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**Center: (5, -2) foci: (3.6, -2),(6.4, -2) **

Answers to HW (Cont): 5.Standard Form: Center: (5, -2) foci: (3.6, -2),(6.4, -2) vertices: (3, -2),(7, -2),(5, -.6),(5, -3.4) 4. Standard Form: Center: (2, -1) foci: (-.2, -1),(4.2, -1) vertices: (5,-1),(-1,-1),(2, 1),(2, -3)

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**Unit Question: How do I recognize, write and graph equations of conic sections?**

How do I write equations of parabolas and graph all of its pieces and parts?

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**PARABOLAS Standard form**

(the distance from the sides of the parabola through the focus)

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Latus focus vertex directrix

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**Parabolas 2 h=0 k=0 p = 1) x2 – 8y = 0 x is squared x2 = 8y 4p = 8**

Vertex: (h,k) (0, 0) opens up Parabolas Axis of symmetry: Focus: (h, k+p) (0, 2) Directrix: y = k – p y = -2 Latus:

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**GRAPH x2 = 8y focus: (0, 2 di vertex: (0, 0) rectrix: y = - axis up )**

8 units across

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**Graph. k = 2 (x – 1)2 = -4(y – 2) h = 1 p =? -4 = 4p (1, 2) focus:**

vertical, down k = 2 (x – 1)2 = -4(y – 2) h = 1 p =? vertex: -4 = 4p (1, 2) focus: = (1, 1) p = -1 directrix: y = 3 latus:

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Graph. (x – 1)2 = -4(y – 2)

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**Graph. horizontal, right (y + 2)2 = 8(x – 3) h = 3 k = -2 p =? 8 = 4p**

vertex: (3, -2) 2 = p focus: = (5, -2) directrix: x = 1 latus:

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**Graph. (y + 2)2 = 8(x – 3) vertex: (3, -2) directrix: x = 1 latus: 8**

focus: (5, -2) semi latus: 4

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**Graph. (x + 1)2 = 12(y + 1) h = -1 k = -1 p =? 12 = 4p (-1, -1) 3 = p**

vertical, up h = -1 k = -1 p =? 12 = 4p vertex: (-1, -1) 3 = p focus: = (-1, 2) directrix: y = -4 axis: x = -1 latus: semi latus: 6

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**Graph. (x + 1)2 = 12(y + 1) vertex: (-1, -1) directrix: y = -4**

latus: 12 focus: (-1, 2) axis: x = -1 semi latus: 6

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Put in standard form 36 36

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**Find the equation of the parabola with focus (2,3) and directrix x=7.**

(y – 3)2 = -2(x – 4.5)

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