Tuesday, December 15, 2009

Conics---WE learned 4 sections to conics.
1. cirlce
2.ellipse
3.hyperbola
4.parabola
This is a conic: x^2 +/- y^2
General form of a conic is: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0
A, B, C, D, E and F are elements of the set of reals. B cannot equal 0
Conics are ALWAYS squared
A circle happens when the A value and the C value are the same.

(x^2 + y^2) = 1 is a small circle
(x^2 + y^2) = 7 is a bigger circle...etc

Ex. Given the general form of the conic equation:
a) Identify the conic
b) State A, C, D, E, F
given... x^2 + y^2 - 8 = 0
a) So this is a circle because both co-efficients are 1.
b) A = 1, C = 1, D = 0, E = 0, F = -8

**An ellipse happens when A and C values are the same sign, but A cannot equal C. An ellipse is a squashed circle, an ellipse is also a subset of a circle.
**A hyperbola happens if A and C have opposite signs.
If the x is positive, than the hyperbola will open horizontally, but if the x is negat
ive the hyperbola will open vertically.
** You have a parabola if one of A or C is the vlaue of 0.
**A circle happens when the A value and the C value are the same.

Tuesday, December 1, 2009

Yesterdays class we leanred about binomial theom-to simplify/ evaluate binomials.
-Pascals Triangle is a triangle that is one big pattern full of numbers, you add the two numbers on top to make the botton number.
-Binomial expansions- some of the exponents is equal to the power of binomial, exponent of term 1 begins with some values as power and decreases by one in each term, exponent of term two appears in second term, increases by one until it matches binomials power, # of terms is one more than the power, coefficients are combinations of power number starts @ nC0 ends with nCn and have symmetry.