Let's say the equation is 2x+5. Underneath the sigma is x=2 and above the sigma is 5. What this means is that you have to solve 2x+5 for numbers from 2-5.
So, first we plug in 2 and get 9.
Then, we plug in 3 and get 11.
Next, we plug in 4 and get 13.
Finally, we plug in 5 and get 15.
Our expanded answer is 9, 11, 13, 15.
Thats about it to expanding sigma notation.
Some things I don't understand are how to use some of the formulas on sequences and series. I also forgot how to graph conics. Thats about it for this blog i guess.
Graphing Conics
ReplyDeleteCIRCLES
-the equation of a circle in standard form
(x-h)^2+(y-k)^2=r^2
where the center is (h,k) and radius=r
-if not in standard form, you must complete the square for both x and y to put in standard form
-give nthe center and point, you can use the distance formula to find the radius
TO FIND THE INTERSECTION OF A LINE AND CIRCLE
-solve the linear equation of a line
-substitute in circle equation
-solve for x
-plug x value in to get y value
*if your x value is imaginary, there is no point of intersection
TO GRAPH A CIRCLE
-find the center and radius
-draw your circle
ELLIPSES
((x-H)^2/(length of X/2)^2)+((Y-K)^2/(length of Y/2)^2)=1
-(h,k)=center
-major axis is the larger denominator
-vertex is on major axis
-focus> smaller#^2=larger#^2-focus^2
focus is on major axis
1. center
2. major axis- bigger denominator (x or y)
3. vertex +/- squareroot larger denominator
4. other intercepts +/- squareroot smaller denominator
5. focus
6. length of major axis 2squareroot larger denominator
7. length of minor axis 2squareroot smaller denominator
8. graph
HYPERBOLAS
((x-h)^2/(length/2)^2)-((y-k)^2/(length/2)^2)=1
-center (h/k)
-major axis is the non-negative denominator
-vertex> +/- squareroot non-negative denominator
-asymptotes> y=+/- (squareroot y/ squareroot x)X
-focus^2= x denom+ y denom
or focus^2= vertex^2+ other denom
TO SKETCH
1. shape
2. center
3. major
4. minor
5. other intercepts (none)
6. focus
7. asymptotes
8. vertex
9. sketch
PARABOLAS
- x=(-b/2a)
-two ways for find the vertex
((-b/2a), f(-b/2a))or complete the square to get in vertex form y=(x+a)^2 +/- b >(-a,b)
-focus (1/4p)=coefficient of x^2
-directrix is P units behind vertex
if opens up, add y value to vertex, if down, subtract y value from vertex
if upens < add x value to vertex, if > subtract x value from vertex