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Begin by reminding them of what we did with simultaneous equations. First, we learned how to solve them (using substitution or elimination). Then we used those exact same techniques to solve the generic version—that is, simultaneous equations where all the numbers were replaced by letters. This, in turn, gave us a formula that could instantly be used to solve any pair of simultaneous equations.

Now we are going to do that same thing with quadratic equations. The “generic” quadratic equation is, of course, a x 2 + b x + c = 0 . Now, we have learned two different ways of solving such equations. The “generic” version is hard to solve by factoring (although it is possible); we are going to do it by completing the square.

Make sure they look over my example of completing the square; this might be a good opportunity for a quick TAPPS exercise. There are other examples in the “Conceptual Explanations” so you could do two TAPPS exercises—that way everyone gets a chance to be the teacher.

Then have them work through the sheet. They should derive the quadratic formula, and then use it.

By the time they are done, they should have two things. They should have the quadratic formula, and a bit of practice using it—so now we have three different techniques for solving quadratic equations. They should also have derived the formula. I always warn them that I will ask for this derivation on the next test: it is not enough to know the formula (although that too is good), you have to be able to derive it.

At the end of class, you may want to talk for just a couple of minutes about the discriminant, in reference to #11. It should be fairly obvious by that point to most of them.


“Homework: Solving Quadratic Equations”

Time for another test!

As always, there is the sample test, which may or may not be assigned as a homework. Then there is the test—on multiplying polynomials, on factoring, and mostly on solving quadratic equations. Make it shorter than my sample ☺

Questions & Answers

What is scarcity.
Npoanlarb Reply
when there is adequate resources
why our wants are limited
Npoanlarb Reply
nooo want is unlimited but resources are limited
and do to that there occurs scarcity and we have to make choice in order to have what we need if need be I will explain more
our wants are not limited but rather the resources
as we know that there are two principle of microeconomics scarcity of resources and they have alternative uses...
yes .....
because our resources are limited./we have a limited resources.
what is demand
Thank Reply
demand is something wt we called in economic theory of demand it simply means if price of product is increase then demand of product will decrease
inverse relationship between demand and price
in microeconomic
demand is what and how much you want and what's your need...
how can one be so with economics even while you have less knowledge in mathematics.
why is it that some products increases everyday by day
Chiamaka Reply
because demand is increase
because demand is increase
but how demand increases?
Because of the Marketing and purchasing power of people.
but how could we know that people's demands have increased everyday by day and how could we know that this is time to produced the products in the market. Is any connection among them
for normal good people demand remain the same if price of product will increase or not
see that some product which increases day by day is comes under normal good which is used by consumer
Seems hot discussing going here
If there are less products demand starts to increase for those products
Economics is really interesting to learn ....
see there is Inferior goods ands normal goods inferior good demand is rarely increase whereas as we talk about normal good demand will absolutely Increase whether price is increase or not
and demand for normal goods increase cause people's income as a while increases time to time
and it might also be that the cost of raw materials are high.
may be
obviously because demand is increasing.....and price is getting low.....
hmmm there is inverse relationship between demand and price
This is because the supply of those products in relation to raw materials are decreasing and they are also necessities. This crate shortage in the market, so sellers will rise the prices of those products.
Importance of economics
Odunayomi Reply
the nature and significance of economics studies
What is demand
Shuaib Reply
deman is amount of goods and services a consumer is willing and able to buy or purchase at a given price.
the willingness and ability of a body to purchase goods nd servicesbis called demand ,so if she/has ability but doesn't have willingness it's not a demand same if she or he has willingness but doesn't has ability it's not a demand too
Demand refers to as quantities of a goods and services in which consumers are willing and able to purchase at a given period of time and demand can also be defined as the desire or willingness and backed by the ability to pay.
What is Choice
Choice refers to the ability of a consumer or producer to decide which good, service or resource to purchase or provide from a range of possible options. Being free to chose is regarded as a fundamental indicator of economic well being and development.
choice is a act of selecting or choosing from the numerous or plenty wants.
demand is want and it is also what you need and able to afford a particular period of time... because demand changes with time.
Demand refers to the ability of the consumer to pay for a particular product at a given price
how does consumer make profit
Clifford Reply
by buying goods in bulk.
Compare and contract the function of commercial bank and the central bank of Nigeria
Akwi Reply
what do think is the difference between overhead costs and prime cost
what is economics
Mohamed Reply
economics is a social science that study's how resources can be used to produce goods and services for society
Economic is a science which studies human behavior as a relationship between ends and scares means which have alternatives uses or purposes.
what is economics
Mohamed Reply
what is the basic economic problem
John Reply
unlimited wants vs limited resources
what economics is all about?
Nomuhle Reply
what is a new paradigm shift
Austen Reply
Paradigm shift it is the reconcilliation of fedural goods in production
fedural? what is that?
factors that affecting economic system
Bemen Reply
what is meant by broadening the tax base?
Fiona Reply
Difference between extinct and extici spicies
Amanpreet Reply
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Source:  OpenStax, Advanced algebra ii: teacher's guide. OpenStax CNX. Aug 13, 2009 Download for free at http://cnx.org/content/col10687/1.3
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