Ok so this week we did conics, ellipses, and hyperbolas. So i guess ill talk about the hyperbolas. For hyperbolas, the formula is (x-h)^2/(length/20^2)-(y-k)^2/(length/2)^2 =1 or -(x-h)^2/(length/2)^2+(y-k)^2/(length/2)^2 =1....i know thats a little confusing. So after u put it in that form, then you will follow steps in order to make a graph:
1. Center (h,k)
2. Major axis is non-negative
3. vertex +/- the square root of the non-negative denominator
4. asymptotes: y+/- sqr. root of y denom/sqr. root of x denom
5. focus^2=x denom + y denom
focus^2=vertex^2+other denom
6. then to sketch the graph make sure u have:
-shape
-center
-major axis
-minor axis
-other interger...if any
-focus
-asymptotes
-vertex
To sketch:
1. Draw a box using the vertex and sqr. root of other denom.
2. Draw diagonals through the box
3. Sketch parabola on each vertex
4. Label foci and asymptotes
Thats basically it. It may seem hard but thats just because there are alot of steps that you have to do. And i dont really have anything i dont understand right now but i do need a little help on changing bases from chapter 5 that i want to make sure i understand so if someone can help...thank you!!
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There are only four simple steps to changing bases
ReplyDelete1)rewrite problem in exponential form
2)take the log of both sides
3)move the variable to the front
4)solve
Ex.
log5of10=x
#1)
5^x=10
#2)
log5x=log10
#3)
xlog5=1
#4)
x=1/log5
okay well changing bases is really easy once you can understand the steps.
ReplyDeletefirst you just set up the logarithim like any normal one.
Ex: log3^7=x
set it up normal
3x=7
next you need to have log on both sides so it would look like this.
log3^x = log7
then you always put your exponent in front of the log.
xlog3=log7
finally you just make x equal both logs.
x=log3/log7.....you put the log on the left as the denominator and the log on the right as the numerator.
i hope this explanation helps you easily remember changing bases!!! :) good luck on the exam.