Solve Word Equations In Quadratic Functions

Solving Quadratic Equations

I'm looking for the equation of a demand curve, which is usually negative sloping, i.e. y = -x. Well, at least that is how it should look. However, I know that y = -x is a linear equation, and that's not exactly what I need. I guess it could be negatively exponential, but I just don't know. Perhaps it might help to give you a few examples of the points on the curve (points are in x:y format)

1) 1,000:400
2) 1,500:300
3) 2,400:200
4) 4,000:100

I should think that the y-intercept would be around 800. It doesn't matter very much whether the curve touches the x-axis, but I would think that the curve would start approaching it around 8,000 or 9,000.

This is actually the curve that I'm trying to find the equation for. Not only that, but then instead of having it in the format of y = ... , I would need it in the format x = ... If you could show me how to find that, I would appreciate it very much.

Answer:

The curve looks like the top right of a circle as I visualise it. You will find it difficult though to work out the exact equation of the curve.

Perhaps this may help put it in the form x=ay^2+bx+c:

y=ax^2+bx+c

y-c=ax^2+bx

You then have to complete the square:

y-c=sq( rt(a)x+(b/(2rt(a)) ) - b^2/4a (test it by multiplying it out. I may have made a mistake)

y-c+b^2/4a= sq( rt(a)x + (b/2rt(a)) )

rt( y-c+b^2/4a ) =rt(a)x + (b/2rt(a))

rt( y-c+b^2/4a)- (b/2rt(a)) = rt(a)x

<rt( y-c+b^2/4a ) - (b/2rt(a)) >/ <rt(a)>= x

A bit difficult to follow, so suggest writing it out on paper. Have used sq to mean ^2 at times and obviously rt(x) to mean the square-root of x. May be some mistakes here so apologise in advance if so, but gives the general idea on how to isolate x

Derbyshire: June Diary - National Review Online Blogs

Derbyshire: June Diary National Review Online Blogs, NY - Jul 1, 2008 You want to understand quadratic equations? Solve a couple hundred of them, by all the different methods — graphical, formulaic, sight-factorization, ...

Dare to Know

What is not taught in School What is Taught: The first mention of man in flight was by Roger Bacon, who drew a flying apparatus. Leonardo da Vinci also conceived of airborne transport and drew several prototypes. What Should be Taught: Ibn Firnas of Islamic Spain invented, constructed and tested a flying machine in the 800's A.D. Roger Bacon learned of flying machines from Arabic references to Ibn Firnas' machine. The latter's invention antedates Bacon by 500 years and Da Vinci by some 700

Handbook of mathematics

Handbook of mathematics Download: pdf1 pdf2 MODUL 1 REVIEW OF INTRODUCTORY MATHEMATICS TERMINOLOGY Summary CALCULATOR OPERATIONS FOUR BASIC ARITHMETIC OPERATIONS Calculator Usage, Special Keys The Decimal Numbering System Adding Whole Numbers Subtracting Whole Numbers Multiplying Whole Numbers Dividing Whole Numbers Hierarchy of Mathematical Operations Summary AVERAGES Average Value Summary FRACTIONS . Proper and Improper Fractions Equivalent Fractions A

Mathematics for Class X : The 4-day study Plan

By: Viji Raj. ______________________________ 4-days to Mathematics exam - Do you think you are ready for the challenge? These days can be either wasted away studying (and in most of the cases, playing and watching cricket) aimlessly or can be utilized in the most effective manner. All you need is a good plan and we are concerned. Our examination experts from TCYonline.com have painstakingly prepared a 4-Day focused plan for the readers of Rediff.com. E-mail it to your friends (whom you do wa

Natl Math Panel: increase algebra in 8th grade

All school districts should ensure that all prepared students have access to an authentic algebra course—and should prepare more students than at present to enroll in such a course by Grade 8. The word authentic is used here as a descriptor of a course that addresses algebra consistently with the Major Topics of School Algebra (Table 1, page 16). Students must be prepared with the mathematical prerequisites for this course according to the Critical Foundations of Algebra (page 17) and the Benchm