How To Quadratic Equations

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

Maths was a pleasant surprise, but it all counts for nothing if ... - Irish Independent

Maths was a pleasant surprise, but it all counts for nothing if ... Irish Independent, Ireland - Jun 6, 2008 I was raring to go and keen not to be caught off guard by some quadratic equation in question two or three. But caught out I was, and when I was shown how ...

School's out, and that's a shame - Houston Chronicle

School's out, and that's a shame Houston Chronicle, United States - Jun 17, 2008 ... session gives KIPP a chance to shore up weaknesses like that, and to give the kids confidence before they tackle harder stuff, like quadratic equations. ...

Unpaid tax is an attack on my sanity - NEWS.com.au

Unpaid tax is an attack on my sanity NEWS.com.au, Australia - Jun 19, 2008 ... epileptic seizures every time a quadratic equation was mentioned, is now expected to be au fait with terms like "deduction", "levy" and "percentage". ...

The test results are in and staff writer Kristen Cates won't be ... - Great Falls Tribune

The test results are in and staff writer Kristen Cates won't be ... Great Falls Tribune, MT - Jun 30, 2008 Talk to me about quadratic equations, and I run the other direction. However, in my reporting days I've boosted my skills by calculating and analyzing Excel ...

The Derivation of "Logistic-shaped" Discovery - The Oil Drum

The Derivation of "Logistic-shaped" Discovery The Oil Drum - Jun 26, 2008 Yet it doesn't match the sigmoid because the equations obviously don't match -- not surprising since my model differs in its details from the Logistic ...

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, ...

Lisa Ryckman on abs workouts - Rocky Mountain News

Lisa Ryckman on abs workouts Rocky Mountain News, CO - Jul 1, 2008 Remember your quadratic equations: what you do to one side, you must do to the other. Mark_Wolf(Q) If you have a back problem - or want to avoid one - what ...

Checking Up On Pythagoras' Midseason Predictions - Bleacher Report

Bleacher Report

Checking Up On Pythagoras' Midseason Predictions Bleacher Report, CA - Jul 1, 2008 It's used to solve quadratic equations, and can tell you what the length is of the third side of the triangle. In baseball, examining a team's offense (runs ...

Math camp gives girls equation on how - Greeley Tribune

Math camp gives girls equation on how Greeley Tribune, CO - Jun 20, 2008 Whether they're studying factorials, binomial coefficients or quadratic equations, it's all good to Caudillo, who loves the challenge of solving problems. ...

Maths? I breakfasted on quadratic equations, but it was a waste of ... - guardian.co.uk

Maths? I breakfasted on quadratic equations, but it was a waste of ... guardian.co.uk, UK - Jun 5, 2008 I breakfasted on quadratic equations, lunched on differential calculus and strolled, arm in arm, with Ronald Searle's square on the hypotenuse. ...

Solution of Quadratic Equation by completing square

How to solve Quadratic Equation by completing squares