Your Algebra Homework Can Now Be Easier Than Ever!

Graphing Quadratic Polynomials

Next Quarter

The class next quarter will be on 10 Monday nights same time
(5:00 PM -8:15 PM) same place (Munroe School)
starting Monday, March 30 and ending Monday, June 8. Class
will not be held on Memorial Day, Monday, May 25 or Monday
April 6.

Today

inequalities in two variables
‘conjugates’ and rational/ real coefficients
Yao and what is ‘ solving an equation
Harel and ‘guess, check, and generalize’
minimax problems
evaluations
questions
exam discussion

Homework analysis

1. Solve the fol lowing system inequalities graphically using your
graphing
calculator and turn in a sketch of the graph with the
region satisfying the inequalities shaded.

What sort of object is the solution?
How can it be described? What are the intersection
points?
calculator screen size; use z-box

Difference of Squares - conjugates

CME 665: 12, 13
Extend to i. Return to 664: 10, 11

Imaginary roots and quadratics

Ask someone to explain the correct solution to CME 664
numbers 10-11.

Yao

Consider the following argument.
Let H be your height, Y be Yao’s height and A be the average
of the two heights, (H + Y )/2. Then H + Y = 2A so that:

or
or

or, adding A 2 to both sides of the equation

Thus, H − A = Y − A or H = Y . You are indeed as tall as
Yao! If you do not think you can ever be as tall as Yao, find
the f law in this argument .

What is a written solution of an
equation/inequality

It is a series of deductions about any number(s) that might
satisfy the
equation
inequality
system of equations
system of inequalities

Moral

If the solution is correct, each line implies the next.
In the case of Yao, the conclusion that if two numbers have the
same
square they are equal was incorrect.
In other cases, (next quarter), the implication may be correct
but The two statements may not be equivalent .
So the result is a candidate solution.
Any solution will satisfy the last line.
Not every number that satisfies the last line has to be a
solution.

Harel

See handout. Taken from Harel’s DNR as a conceptual
framework.

Maximizing area

CME 710 problem 8
Look at problem 10 on that page.
Make up a similar but more complicated problem where there
are different constraints on the perimeter (including internal
walls) but the area is maximized.

Course Summary for Exam

Each topic may be addressed either in a concrete situation or
as pure mathematics problem.

Solution of systems of linear equations .
Graphs of linear equations
modeling
What does it mean to have no or infinitely many solutions
Solution of systems of linear inequalities ( in one unknown )
Solution of systems of linear inequalities (in two
unknowns)
absolute value including solutions of inequalities and
equations in one or two variables
Finding exact solutions; finding approximate solutions
graphically
Normal forms for linear and quadratic equations
Properties of quadratic functions and their graphs
Solutions of quadratic equations (factoring, completing
the square, quadratic formula )
representing functions by formulas, graph, table
Transformation of quadratics and the effect on the graph
understanding the logic of equation/inequality solutions
the zero product property and other properties of the real
numbers
minimizing or maximizing quadratic functions
the function notion

Find at least one problem from the homework or from the CME
text that addresses each of these topics and solve it. Some of
the topics are broad enough so that you should look at several
different problems. Look for connections between the various
topics. Try to see how the same concrete situation can be
solved using different topics.

Prev Next

Start solving your Algebra Problems in next 5 minutes!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of December 12th you will pay only $39.99 instead of our regular price of $74.99 -- this is $35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:



Algebra Helper can solve problems in all the following areas:

  • simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
  • factoring and expanding expressions
  • finding LCM and GCF
  • (simplifying, rationalizing complex denominators...)
  • solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
  • solving a system of two and three linear equations (including Cramer's rule)
  • graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
  • graphing general functions
  • operations with functions (composition, inverse, range, domain...)
  • simplifying logarithms
  • basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
  • arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath
Check out our demo!
 
"It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..."
C. Sievert, KY
 
 
Sofmath
19179 Blanco #105-234
San Antonio, TX 78258
Phone: (512) 788-5675
Fax: (512) 519-1805
 

Home   : :   Features   : :   Demo   : :   FAQ   : :   Order

Copyright © 2004-2017, Algebra-Answer.Com.  All rights reserved.