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)=x^{2}-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:

x^{3}-3x+4e^{x}=17x^{2}

Practiced finding roots for different functions.

(x^{3}-6x^{2}-2x+5)(e^{-x}-0.5)=x

y=lnx —> domain x>0

y=ln(1+x^{2})=0

y=ln(x+2) 2+x>0

x>-2

y=(3x^{2}-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.