Warmup Alg 2 16 April 2012

1. WarmupAlg216 April 2012

2. Agenda • Don't forget about resources on mrwaddell.net • Section 9.1: Intro to Conic Sections • Distance and midpoint formula • Recognizing Conic Sections

3. Section 9.1: Introduction to Conic Sections

4. What are Conic Sections?

5. Where are Conic Sections found? The St. Louis Arch is an example of sort of a parabola.

6. Where are Conic Sections found? Ferris wheels are circular. They were also invented by George Ferris, who lived in Carson City for a while (and whose father was a founder of Knox College where I went to college!)

7. Where are Conic Sections found? St. Paul’s Cathedral, the Washington Capitol and the Mormon Tabernacle Choir are all Ellipses. If you are at one foci, you can hear what is happening at the other.

8. Where are Conic Sections found? How many hyperbolas and circles here?

9. The Conics Circles Hyperbolas Parabolas Ellipses

10. Distance formula • Find the missing side of the triangle. a2 + b2 = c2 62 + 82 = c2 6 8

11. Distance formula • Find the missing side of the triangle. 6 a2 + b2 = c2 62 + 82 = c2 8

12. Distance formula • Find the distance in RED (-2,7) a2 + b2 = c2 (4- -2)2 + (-1- 7)2 = c2 (4,-1)

13. The Distance Formula • To find the distance between any two points (x1, y1) and (x2, y2), use the distance formula: Distance = Hmm, kind of looks like the Pythagorean Theorem!

14. The Midpoint Formula • The midpoint of a line is halfway between the two endpoints of a line. • To find the midpoint between (x1, y1) and (x2, y2), , use the midpoint formula:

15. The Midpoint Formula • To say it another way: • Find the AVERAGE of the X’s and the AVERAGE of the Y’s!

16. Practice Find the distance between (-4, 2) and (-8, 4). Then find the midpoint between the points.

17. Classify a Triangle using the Distance formula • If a triangle has: • 3 sides the same: • 2 side the same: • No sides the same: Then it is: Equilateral Isoceles Scalene

18. Assignment • Section 9.1: 6 – 14, 27 - 30