What Is A Quadratic Equation In Vertex Form

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

Pseudorandomness for Polynomials

I am currently in Hong Kong for my second annual winter break visit to the Chinese University of Hong Kong. If you are around, come to CUHK on Tuesday afternoon for a series of back-to-back talks by Andrej Bogdanov and me. First, I'd like to link to this article by Gloria Steinem. (It's old but I have been behind with my reading.) I believe this presidential campaign will bring up serious reflections on issues of gender and race, and I look forward to the rest of it. Secondly, I'd like to talk

Math A30 Relations and Functions

Subject: Math A30 Unit: Relations and Functions Topic: Quadratic Functions - Standard Form Objectives: Evergreen Curriculum Website: Graphing Calculator This website contains a free online graohing calucaltor. Depending on the budget in your school some may not have access to handheld gaphing calculators, therefore websties like this can benefit your students. I would use the online graphing calcualtor to assist students in a discovery lesson in which the students will conjecture the applicat

Schedule for the week of 2/11

Mon: Graphing parabolas worksheet Tue: Finding the x-intercepts of parabolas Wed and Thu: using the vertex form of a quadratic equation (done together in class)

Math Midterm #2(HELP ME!!!)

Friday, February 22, 2008 at 1pm Pacific Standard Time I take midterm # 2 in Math 97. I could use all your high math skills vibes sent this way. Please. I have to pass this class to move onto Math 156 which I need to be all finished with my AA. Prayers are extremely welcome. I think a miracle may be needed. ax^2+bx+c=0 is the quadratic equation. -b+/-the sq. root of (b)^2-4(a)(c)/2(a) is the quadratic formula. x=-b/2a is the formula to find the vertex of the parabola. Complex numbers need t

Minutes: 02/27/08

Minutes: 02/27/08 Orchids Gonshor: Glad to be starting a new unit. Fuller: Looking forward to working on the new hybrid year 4 course. Mickey: Has achieved peace in the PLC. Marchetti: Excited about working with the data. Discussion of changes to IMP2 to meet district and testing needs: Fireworks moved to Year 2 Pit moved to Year 2 Skill Supplements Curriculum map developed to fill gaps (IMP materials not a perfect fit with district curriculum) CSAP practice booklets Honors vs

Quiz on Thursday!

Hello everyone! Throughout this week, make sure you continually check up on your skills so that you are fully prepared for the Mid-Chapter 25 point quiz on Thursday. Just in case you can’t find your unit check list, here are the following concepts that may / will appear on the quiz. Please use this forum space to discuss quiz topics and ask your classmates questions about quiz concepts. Good luck!! ______1. Determine if an expression is a polynomial. If so, then write it in general form a

ZOMG FOURTH HOUR MATH BLOG!!!!111!1!1!11!1shift+111111eleventyoneoneone

ZOMG FOURTH HOUR MATH BLOG!!!!111!1!1!11!1shift+111111eleventyoneoneone Posted by Andy So… Here’s the 4th hour’s attempt to be back on the 1st page of the blog again! And an attempt to make our quarter journal grades not die. Ok, here goes… Today we did a sketchpad project. The basis of it is that if you have a polynomial with clearly defined zeros because it’s in factored form, you can figure out the multiplicities of those zeros, and therefore the degree of the polynomial, by looking at th

Day 131

Algebra: Chapter 12-4, p 552 Quadratic Functions A quadratic function is defined by `f(x) = ax^2 + bx + c`. To make it easier, just replace the `f(x)` with `y` and treat as you have done in the past. With a function in standard form `ax^2 + bx + c`, the vertex is `-b/(2a)` and the axis of symmetry is `x = -b/(2a)`. The vertex is the point on the PARABOLA where the slope changes sign from positive to negative or vice-versa. The axis of symmetry, you recall, is the line when the parabola can

Standards - Content Strand

Integrated Algebra Performance Indicators – CONTENT STRAND Number Sense and Operation Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems. Students will understand meanings of operations and procedures, and how they relate to one another. A.N.1 Identify and apply the properties of real numbers (closure, commutative, associative, distributive, identity, inverse) Note: Students do not need to identify groups and fields,