This document discusses key properties of parabolas in vertex form, including the vertex, line of symmetry, focus, directrix, and latus rectum. It provides examples of writing equations of parabolas in vertex form and extracting the vertex, axis of symmetry, and other properties. The vertex is the point (h, k) and the line of symmetry is x=h or y=k depending on the form of the equation. The focus and directrix define the parabola such that all points on the curve are equidistant from these elements.

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

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

3. focuslatus rectumdirectrixAll points on the parabola are equidistant from the focus and the directrix.

4. y = a(x – h)2 + kfocus1 4asame distancedirectrix

5. y = a(x – h)2 + kfocuslatus rectum1 alength =directrix

6. Pg 422

7. 4(y – 2) = (x + 3)24y – 8 = (x + 3)24y = (x + 3)2 + 8 4 4y = ¼ (x + 3)2 + 2a = ¼ h = -3k = 2y = a(x – h)2 + k

8. y = ¼ (x + 3)2 + 2vertex: (-3, 2)axis of symmetry: x = -3a = ¼distance 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 4x = ¼ (y – 1)2 + 3x = a(y – k)2 + h+1 – 1 +13 +13

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