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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
If c is the cost function for a particular product, find the marginal cost functions and their
values at x=10 a. c(x) = 800+ 0.04x + 0.0002x² b. c(x) = 250 + 100x + 0.001x²
how can I find set theory
how can I find set theory
Jarvis
is there an error on the one about the dime's thickness? says 2.2x10⁶=0.00135 m
hi, interested in algebra
how to reduce an equation?
Makan
by manipulation of both side
Al
9(y+8)-27 is 9y+45.
Why can't you reduce that to y+5? I know that's wrong but can't explain why
when you reduce an equation to its simplest terms, you can't change the value of the equation. reducing it to y + 5 is equivalent to dividing it by 9 which changes the value. you can multiply it by 1 or 9/9 which would give 9(y + 5). multiplying it by one does not change the value.
Philip
Given a polynomial expression, factor out the greatest common factor.
WHAT IS QUADRATIC EQUATION?
WHAT IS SYSTEM OF LINEAR INEWUALITIES?
Charles
WHAT IS SYSTEM OF LINEAR INEWUALITIES?
Charles
what are equations?
Charles
Definition of economics according to
karl Marx
Thomas malthus
Jeremy bentham
David Ricardo
J.K
Rakiya
Please help me is assignment
Rakiya
The 47th problem of Euclid
Kenneth
show that the set of all natural number form semi group under the composition of addition
what is the meaning
Dominic
explain and give four Example hyperbolic function
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the
fraction, the value of the fraction becomes 2/3. Find the original fraction.
2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2
-------------- = _
x + 9 + 6 3
x + 6 3
----------- x -- (cross multiply)
x + 15 2
3(x + 6) = 2(x + 15)
3x + 18 = 2x + 30 (-2x from both)
x + 18 = 30 (-18 from both)
x = 12
Test:
12 + 6 18 2
-------------- = --- = ---
12 + 9 + 6 27 3
Pawel
2.
(x) + (x + 2) = 60
2x + 2 = 60
2x = 58
x = 29
29, 30, & 31
Pawel
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
Q2
x+(x+2)+(x+4)=60
3x+6=60
3x+6-6=60-6
3x=54
3x/3=54/3
x=18
:. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
Mark = x,. Don = 3x + 1
x + 3x + 1 = 113
4x = 112, x = 28
Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
please can go further on polynomials quadratic
Abdullahi
I need quadratic equation link to Alpa Beta
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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