1. Lesson Objective: IWBAT to graph a parabola, find the focus and the directrix, and write the equation. Parabolas

2. Guiding Question: How can I graph a conic section? Conic Section: Graph formed by the intersection of a double cone and a plane. The four conic sections are parabola, circle, ellipse, and hyperbola.

3. Guiding Question: How can I graph a conic section? Definition of parabola: set of all points equidistant from a fixed line and a fixed point. Fixed Point: Focus Fixed Line: Directrix.

4. Guiding Question: How can I graph a conic section? Recall the vertex form of a quadratic Vertex is (h, k) Focus is (h, k+p) Directrix is y = k-p • Recall the distance formula between 2 pts. • This is how you show 2 pts. are equidistant from the parabola.

5. Guiding Question: How can I graph a conic section? p = and Vertex Form • Standard Form of a Parabola (x - h)² = 4p(y - k) What do you notice about how they are similar?

6. Guiding Question: How can I graph a conic section? • The focal widthis a segment that goes through the focus that is 4p units long. It is used to help draw the graph. • Example 1.

7. Guiding Question: How can I graph a conic section? • Graph the following

8. Guiding Question: How can I graph a conic section? • What if they switched?

9. Guiding Question: How can I graph a conic section? • Assignment: Worksheet