1. Conic Sections - Parabolas
Chapter 8, Section 1

2. About Parabolas Definition
The set of all points in a plane equidistant from a given fixed line called the directrix and a given fixed point called the focus
The distance from the focus to the vertex is the same as the distance from the vertex to the directrix
The vertex is ½ the distance between the focus and the directrix
Axis of symmetry is a line through the focus and vertex that is perpendicular to the directrix

3. About Parabolas, continued…
The vertex is the intersection of the axis of symmetry and the parabola
is the distance from the focus to the vertex
is the focal width of the parabola
The length of a chord through the focus and is perpendicular to the axis

4. Horizontal Parabolas Vertex: (h,k) Focus: (h+p,k)
Axis of symmetry: y=k
Directrix: x=h-p
If p>0, opens right
If p<0, opens left

5. Vertical Parabolas Vertex: (h,k) Focus: (h, k+p) Axis of symmetry: x=h
Directrix: y=k-p
If p>0, opens up
If p<0, opens down

6. General Form of parabolas

7. Examples – find the vertex, focus, directrix, axis of symmetry

8. Examples – write the equation in standard form

9. Classwork/Exit Slip
Find the vertex, focus, directrix, and axis of symmetry:
Write the equation in standard form:
Homework: Page 639, #12, 15-20, 25, 26, 49-52