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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
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Omeprazole
Cimetidine / Tagament
For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
how does the stomach protect itself from the damaging effects of HCl
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
function of digestive
Ali
what is the normal body temperature
please why 37 degree selcius normal temperature
Mark
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
how does Lysin attack pathogens
Diya
I information on anatomy position and digestive system and there enzyme
anatomy of the female external genitalia
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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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