Week 3 (January 29th-February 2nd)
Christine Quinn
Megan Ozlek
We pretty much own this assignment.
Day 6: January 29, 2007
Today, we used the TI-89 to simulate boundaries, shifts, and changes in signs for the graphs of quadratic functions.
Quadratic Function: 2 roots, 1 root, or no roots
Example: f(x)=x2-3x+1
Use: Zoomfit to see the general idea of where the root is located. Then, continue by using ZoomIn to get closer and closer to the root.
Use: Trace (on the calculator F2) to see if there is a sign change.
We found that the root is between 0.3797 and 0.3877.
To find approximate root, use these steps:
Math (F5) -> zero -> Left bound -> Right bound -> Enter -> zero= x= 0.38197 and y=0
Use the same procedure to find the other root: x= 2.61803
We continued by moving to our excel spreadsheets to examine how the graphs of particular functions are manipulated by changing that function.
f(x)=-x+sinx and f(x)=-x+cosx : these graphs simply shifts by pi/2 when graphed.
Then, we looked at how technology such as the calculator may not say the type of answer we want.
f'(x)=-1-sinx
0= -1-sinx
sinx=-1 -> x= -pi/2 or +pi/2 <- this is the maximum but the calculator does not say something for that.
Day 7: January 31, 2007
We continued to look at the way graphs shift as they are manipulated and used our excel worksheet to illustrate those changes.
Equation One: y=xe^(-x) - 2
Type in excel: =(B6)*Exp(-B6)-2
Use excel to find roots of function.
To enter pi in Excel: pi()
Equation Two: y= x-tanx
tanx=x
-the tangent graph will be along the line y=x.
-the graph has unlimited roots because tangent always goes from positive infinity to negative infinitity.
-tangent function graph also has vertical asymptotes - continuous roots.
Learned how to use macro(tools-macro-record new macro). Then applied what we learned in order to zoom in on each root: Ctrl + R
Day 8: February 2, 2007
We have a quiz on finding the roots of a function:
x3-3x+4ex=17x2
Practiced finding roots for different functions.
(x3-6x2-2x+5)(e-x-0.5)=x
y=lnx —> domain x>0
y=ln(1+x2)=0
y=ln(x+2) 2+x>0
x>-2
y=(3x2-2x+4)(ln(3x)-1)
2 roots^ 1 root^
We have an online quiz due Monday, February 5, 2007.
We have to send an e-mail explaining the Fundamental Theorem of Algebra by Monday.
