# 4.5 The "generic" quadratic equation

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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, $a{x}^{2}+bx+c=0$ . 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.

## 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 ☺

What is scarcity.
Fiona
why our wants are limited
nooo want is unlimited but resources are limited
Ruchi
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
Moses
as we know that there are two principle of microeconomics scarcity of resources and they have alternative uses...
Ruchi
yes .....
Mathias
because our resources are limited./we have a limited resources.
Ijeoma
what is demand
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
Ruchi
inverse relationship between demand and price
Ruchi
in microeconomic
Ruchi
demand is what and how much you want and what's your need...
Shikhar
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
because demand is increase
Ruchi
because demand is increase
Patience
but how demand increases?
Aziz
Because of the Marketing and purchasing power of people.
AmarbirSingh
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
yaqoob
for normal good people demand remain the same if price of product will increase or not
Ruchi
see that some product which increases day by day is comes under normal good which is used by consumer
Ruchi
Seems hot discussing going here
Shamamet
If there are less products demand starts to increase for those products
Shamamet
Economics is really interesting to learn ....
Shamamet
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
Ruchi
and demand for normal goods increase cause people's income as a while increases time to time
Abhisek
and it might also be that the cost of raw materials are high.
ATTAH
may be
Ruchi
obviously because demand is increasing.....and price is getting low.....
Shikhar
hmmm there is inverse relationship between demand and price
Ruchi
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.
Abdul
Importance of economics
the nature and significance of economics studies
Deborah
What is demand
deman is amount of goods and services a consumer is willing and able to buy or purchase at a given price.
Sainabou
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
Gul
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.
Yeah
Mathias
What is Choice
Kofi
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.
Shonal
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.
Ijeoma
Demand refers to the ability of the consumer to pay for a particular product at a given price
Abdul
how does consumer make profit
Ijeoma
Compare and contract the function of commercial bank and the central bank of Nigeria
what do think is the difference between overhead costs and prime cost
Abdoulkarim
what is economics
economics is a social science that study's how resources can be used to produce goods and services for society
Nathan
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
what is the basic economic problem
rules
unlimited wants vs limited resources
Nathan
what is a new paradigm shift
Paradigm shift it is the reconcilliation of fedural goods in production
Shyline
fedural? what is that?
Aziz
factors that affecting economic system
crux
Shyline
what is meant by broadening the tax base?
Difference between extinct and extici spicies
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