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- Equations and inequalities
- Quadratic equations
For the following exercises, determine the discriminant, and then state how many solutions there are and the nature of the solutions. Do not solve.
For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state
No Real Solution .
Technology
For the following exercises, enter the expressions into your graphing utility and find the zeroes to the equation (the
x -intercepts) by using 2
nd CALC 2:zero. Recall finding zeroes will ask left bound (move your cursor to the left of the zero,enter), then right bound (move your cursor to the right of the zero,enter), then guess (move your cursor between the bounds near the zero, enter). Round your answers to the nearest thousandth.
To solve the quadratic equation
we can graph these two equations
and find the points of intersection. Recall 2
nd CALC 5:intersection. Do this and find the solutions to the nearest tenth.
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To solve the quadratic equation
we can graph these two equations
and find the points of intersection. Recall 2
nd CALC 5:intersection. Do this and find the solutions to the nearest tenth.
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Extensions
Beginning with the general form of a quadratic equation,
solve for
x by using the completing the square method, thus deriving the quadratic formula.
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A person has a garden that has a length 10 feet longer than the width. Set up a quadratic equation to find the dimensions of the garden if its area is 119 ft.
2 . Solve the quadratic equation to find the length and width.
7 ft. and 17 ft.
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Abercrombie and Fitch stock had a price given as
where
is the time in months from 1999 to 2001. (
is January 1999). Find the two months in which the price of the stock was $30.
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Suppose that an equation is given
where
represents the number of items sold at an auction and
is the profit made by the business that ran the auction. How many items sold would make this profit a maximum? Solve this by graphing the expression in your graphing utility and finding the maximum using 2
nd CALC maximum. To obtain a good window for the curve, set
[0,200] and
[0,10000].
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Real-world applications
A formula for the normal systolic blood pressure for a man age
measured in mmHg, is given as
Find the age to the nearest year of a man whose normal blood pressure measures 125 mmHg.
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The cost function for a certain company is
and the revenue is given by
Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of
x (production level) that will create a profit of $300.
The quadratic equation would be
The two values of
are 20 and 60.
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A falling object travels a distance given by the formula
ft, where
is measured in seconds. How long will it take for the object to traveled 74 ft?
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A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 378 ft
2 . Find the width of the walkway if the garden is 12 ft. wide by 15 ft. long.
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An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students,
who contracted the flu
days after it broke out is given by the model
where
Find the day that 160 students had the flu. Recall that the restriction on
is at most 6.
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Questions & Answers
it is the relatively stable flow of income
what is circular flow of income
branches of macroeconomics
what is Flexible exchang rate?
is gdp a reliable measurement of wealth
introduction to econometrics
Why is unemployment rate never zero at full employment?
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
what is the problem of macroeconomics
Yoal
Economic growth
Stable prices
and low unemployment
Ephraim
explain inflationcause and itis degre
increase in general price levels
WEETO
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
nawalparasi district
from belatari
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
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Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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