1. Vertex form (standard form) for the equation of a parabola y = a(x – h)2 + k x = a(y – k)2 + h Vertex: (h, k) Vertex: (h, k) Line of symmetry: x = h Line of symmetry: y = k

2. Graph x = 2y2 + 8y + 9 x = (2y2 + 8y ) + 9 x = 2(y2 + 4y + 4) + 9 - 8 x = 2(y+ 2)2 + 1 Vertex: (1, -2) Axis of symmetry: y = -2 Opens to the right

3. focus latus rectum directrix All points on the parabola are equidistant from the focus and the directrix.

4. y = a(x – h)2 + k focus 1 4a same distance directrix

5. y = a(x – h)2 + k focus latus rectum 1 a length = directrix

6. Pg 422

7. 4(y – 2) = (x + 3)2 4y – 8 = (x + 3)2 4y = (x + 3)2 + 8 4 4 y = ¼ (x + 3)2 + 2 a = ¼ h = -3 k = 2 y = a(x – h)2 + k

8. y = ¼ (x + 3)2 + 2 vertex: (-3, 2) axis of symmetry: x = -3 a = ¼ distance from vertexto focus = = 1 distance from vertexto directrix = 1 1_4(¼) Length of latus rectum: 1 = 4 units¼

9. 4x – 13 = y2 – 2y 4x – 13 = (y2 – 2y ) 4x = (y – 1)2 + 12 4 4 x = ¼ (y – 1)2 + 3 x = a(y – k)2 + h +1 – 1 +13 +13

10. x = ¼ (y – 1)2 + 3 vertex: (3, 1) axis of symmetry: y = 1 a = ¼ distance from vertexto focus = = 1 distance from vertexto directrix = 1 1_4(¼) Length of latus rectum: 1 = 4 units¼