Quadratic Definition and 965 Threads

Homework Statement Sketch the graph of y=x^2 and graph y=1/2(x+4)^2 -5 Homework Equations The Attempt at a Solution So, This is the method I use for vertical compression/expansion Step pattern of a parabola at y=x^2 is 1,3,5 Start at vertex, go out by one, go up by 1...

Homework Statement Dang it! More recurrence relation problems, but this time it’s due to a quadratic equation. Q. In the sequence u1, u2, u3,…,un, u1 = 0, u2 = 3, u3 = 12 and un = a + bn + cn2 Find the values of a, b and c. Homework Equations Provided at back of book…...

Homework Statement Very embarrassing that I had problems with this. I managed to solved it at the end, but I am posting this for two reasons 1) I like someone else to work it out in a different method, I wnt to see what other approaches there are 2) Whether mine is taking too long or not. I...

Homework Statement Find the zeros of the quadratic equation? Homework Equations P(x)=4(x+7)^2+(x+7)-3 The Attempt at a Solution I substituted and made it 4u^2+u-3 ?? Then after that I factor then back substitute?? I'm not sure how to back substitute tho.

quadratic inequality--interval notation.. Homework Statement 2x^2<-x+10 Solve inequality and put into interval notation Homework Equations interval notation The Attempt at a Solution I don't even know where to start. I set it equal to zero -2x^2-x+10=0

Hi, I have a problem with splitting x4 + 1 into real quadratic factors. How can this be done? Cheers.

Hi there! I'm working on analyzing some data from an experiment, and you can see a graph of some of the results in the attached .jpg image. I've done both a linear and a quadratic fit on the data points, weighted to error bars (the red lines are the fits). I use percents in the graph, but I'd...

"Find the rule of correspondence for a quadratic equation that is the same shape as y=x^2, with the only given information being x-intercepts at (-3, 0) and (1, 0)." I cannot for the life of me figure this out, and it's making me feel extremely stupid. I know the answer to the question is y=...

Given an equation in the form 0 = ax2 + bx + c, why is it not possible to simply differentiate both sides, and produce 0 = 2ax + b, and solve for x, instead of going through the drudgery of the quadratic equation? My knowledge of calculus tells me that it is because 0 = ax2 + bx + c is not a...

But seriously, why am I getting the wrong answer here: 4x^2+10x= 5 4x^2+10x - 5 = 0 x=\frac{-10+\sqrt{180}}{8} Answers Incorrect: 3.461 and -23

How do I clear fractions in problems like this and set it up for the quadratic formula: \frac{1}{x-1}+\frac{2}{3}=\frac{2}{x-3} I would like to set this up to be solved with the quadratic formula. Also, is it true that the formula can solve all quadratic equations?

Is there a way to input values within a certain range into my calculator? For example, if I come across something like this: "Draw a curve of y=2x between the values x=+3 and x=-3. From the curve write down the following values: etc, etc, etc" How can I make it graphic w/in a certain range?

Homework Statement A (complex) solution to the quadratic equation of the form z^2 + α z + β = 0, is z = 1 + i. (where α and β are real numerical constants), Write down the other solution and hence determine the values of α and β. Homework Equations The Attempt at a Solution this question...

Homework Statement How do you use the Quadratic Formula to solve First Order ODE? For example, I am given this integration (see attachment at the bottom). Homework Equations The Attempt at a Solution I integrated both sides but I do not know where to go from there (see attachment at the...

Homework Statement For the quadratic form x2-2xy+2yz+z2: a) Find a symmetric matrix that allows the quadratic form to be written as xTAx. b) Determine if the critical point at the origin is a minimum, maximum, or neither. c) Find the points for which the quadratic form achieves its...

could someone please explain briefly what the problem is with my method of finding such canonical forms. The method we've been taught is to find the canonical form by performing double row/column operations on the matrix representation of quadratic form until we get to a diagonal matrix, and...

I am told that the set of positive definite quadratic forms on R^2 has a metric that turns it into H x R where H is the hyperbolic plane. Can you describe this metric? * As a space the forms are viewed as GL(2,R)/O(2).

Hey, I have a set of quadratic equations in the form of: ax^2 -bxy + cy^2 = d ax^2 -bxz + cz^2 = d ay^2 -byz + cz^2 = d where a,b,c,d are given constants. I am really stuck trying to figure out the values of x,y,z :confused: My previous trial, was attempting to solve it as a...

y^2= 1- 2x^2 im supposed to put it in x^2/a^2 + y^2/b^2 = 1 to find the foci and so forth. when i try to set it up i get 2x^2 + y^2 = 1. I am not sure where to go from here. if i multiply or divide to set the problem up properly the 1 will change and my equation will be messed up. can...

1. An Acapulco diver dives into the sea from a height of 35 m. His height h metres t seconds after leaving the cliff is given by h=-4.9t^2+t+35. How long is it until he reaches the water? How long does it take him to fall from 35 m to 25 m? 2. (-b +/-(sqrt)b^2-4ac)/2b 3. I don't have any work...

Hello. This is 2D with arbitrary orientations. I have a quadratic curve segment defined by 2 end points and another one in between. I can find lots of other points along this curve. I want to find a close-enough elliptic spline. It is defined by 2 end points and the point of intersection...

This is something that's been bothering me for a while... If quadratics are any polynomials that have a degree of 2, then would that make the following equations quadratics (I don't know what all of them are for by the way, they're just equations I'm pulling from my math book which doesn't...

Hi, Everyone: I have a quadratic form q, defined on Z⁴ , and I know the value of q on each of the four basis vectors ( I know q is not linear, and there is a sort of "correction" for non-bilinearity between basis elements , whose values --on all pairs (a,b) of...

Hey all, I was bored as heck with my internet down and started scribbling some random math stuff. I'm sure what I've come up with is old news to most but I found some interesting properties in the following proof and I'm curious what my fellow physicsforums users can come up with to see what...

Homework Statement I'm having major issues working out how to integrate \int\frac{1}{F-Gx+x^{2}}dx , where F and G are constants. Homework Equations The Attempt at a Solution Maple tells me it is an inverse hyperbolic tangent of some description, and I know I have to...

This is what I understand right now: The stark effect is when we perturb a system with hamiltonian H_0 by applying a constant electric field, so that H = H_0 - F D_z where F is the field, aligned in the z direction, and D_z is the z-component of the induced dipole. The first order...

Hi all, Hope some here can help me with this math problem. Given, y1 = ax^2 + b. y2 = cos (y1). where a and b are constants. Is y2 periodic with respect to x.? Visually using example grpah, seems to be periodic. How do u find the exact period of such a function? Thanks in advance...

I want to find value for m for which: 4m2 - 12m > 0 Say I do this algebraically: 4m(m-3) > 0 so m > 0 or m > 3 The answer however is 0 < m and m > 3, I know this as a fact as I have looked graphically. So, my question is, when done algebraically, how do I get 0 < m instead of m...

Homework Statement (a) Estimate the terminal speed of a wooden sphere (density 0.870 g/cm3) falling through air, if its radius is 8.00 cm and its drag coefficient is 0.500. (The density of air is 1.20 kg/m3.) (b) From what height would a freely falling object reach this speed in the absence...

Hi everyone! I need to find the antiderivative(1/(3x^2 + 2)) but am not sure which approach to take. I have tried the following only to arrive at a dead end. 1/3x2+2= .5(1/(3(x/sqrt(2))2+1)= (1/6)(1/((x/sqrt(6))2+(1/3)) Thank you so much!

Homework Statement if roots of the equation ax^2+bx+c=0 be the form of p/(p+1) and (p-1)/p,the the value of (a+b+c)^2 is? Homework Equations The Attempt at a Solution

Prove that t2+2t+1,t2+t, t2+1 is a basis for the space of quadratic polynomials P(2).

Homework Statement I just would like to know how would I isolate x in a quadratic equation such as y = x(3-x). Homework Equations quadratic equation. The Attempt at a Solution I don't think you can use completing square in this, and quadratic equation doesn't really...

Homework Statement Show x^2 + (p+1)/4 \equiv 0 (\mod p) where p \equiv 3 (\mod 4) and p is prime is not solvable.Homework Equations Legendre's and Jacobi symbol, congruencesThe Attempt at a Solution Noticing that x^2 \equiv -(k+1) (\mod p) when p = 4k + 3 ? Now (-1/p)(k+1/p) should tell use...

Homework Statement You throw a penny straight up at a speed of 10m/s from a height of 1 m. 1. what's it position 0.5 seconds after it is released? - i found that value to be 4.775 m 2. how high up does it go? = 6.10 m 3. what is its speed when it hits the ground? =? 4. how long is the...

http://www.cs.odu.edu/~toida/nerzic/content/problem_solving/problem_solving.html example 3 ========================================= Quote Problem: Given that a, b, and c are odd integers, prove that equation ax2 + bx + c = 0 can not have a rational root. Understanding the Problem: This is a...

Homework Statement Solve 2kx^2 - (k+1)x + 4 by completing the square Homework Equations 2kx^2 - (k+1)x + 4 The Attempt at a Solution What I have so far: -> x^2 - (k+1/2k)x + 4/2k = 0 -> x^2 - (k+1/2k)x + ((k+1/2k)/2)^2 - ((k+1/2k/2)^2 + 2k = 0 -> x^2 - (k+1/2k)x +...

While solving an problem , i came to this quadratic x2- 8x +4 =0 I couldn't break up 8x so i to solve it like this, x= {-(-8)+√(8 2+ 4x1x4)}/2x1,{-(-8)-√(8 2+ 4x1x4)}/2x1 but the answers are coming way too absurd and negative. The actual problem is: "A hollow right cylinder of...

Homework Statement Find the exact (surd) answer Homework Equations -2kx^2 + 4x +6k = 0 The Attempt at a Solution Attempt 1 (quadratic formula method) -2kx^2 + 4x +6k = 0 -> -(-2) +- sqrt((-2)^2 - (4 x k x -3k)0 / 2k -> 2 +- sqrt(4+12k^2) / 2k -> 2 +- sqrt(4(1+3k^2)...

Homework Statement Solve the quadratic equation z^2 + 4(1 + i(3^0.5))z - 16 = 0 Homework Equations The Attempt at a Solution I think I've done this correctly, I just wanted to verify. I've only done the solution for k=0...

Problem: A = n by m matrix x = m by 1 vector y = n by 1 vector C = c by m matrix E = e by m matrix Alpha, gamma and theta are constants. norm(Ax-y) = min subject to: norm(Cx) = alpha norm(Ex) = gamma transpose(Cx)*Ex = (alpha^2)*(gamma^2)*cos(theta) I read a paper on how to do this with 1...

Homework Statement A coin it thrown from the top of a building, and its height in metres above the ground after 0, 1, 2, 3, 4, and 5 seconds is recorded as follows: {200, 203, 202, 197, 188, 175}. algebraically determine the function that describes this situation and use it to determine when...

Homework Statement Three point charges lie along the x axis. The positive charge q1 = 15.0uC and is at x = 2.00m (2.00 away from the origin), the positive q2 = 6.00uC is at the origin. The net force on q3 which is between q2 and q1 is 0. What is the x coordinate of q3? solution My...

I am trying to find the domain of this function f(x)=sqrt(x^2 - 2x +5). i am supposing that y=x^2 - 2x +5 and y must be greater of equal to 0. in otherwords where the graph is touching or above x axis. to find where the graph is touching x-axis i am trying to find the x intercept and i get...

http://img717.imageshack.us/img717/4029/screenshot20110106at123.png i don't know how to construct an algebraic proof from this or how to attempt it. is there anything obvious which i missed? thank you

Homework Statement http://img717.imageshack.us/img717/4029/screenshot20110106at123.png i don't know how to construct an algebraic proof from this or how to attempt it. thank you Homework Equations The Attempt at a Solution

Homework Statement True or False and Why? "The sum of two quadratic forms in three variables must be a quadratic form as well." Homework Equations q(x_1,x_2,x_3)=x_1^2+x_2^2+x_3^2+x_1x_3+x_2x_3 The Attempt at a Solution I am definitely missing something. To me this is a...

Can someone tell me how to approach this problem? Find the period of oscillation of a particle of mass m, constrained to move along the x-axis, with a potential V(x)= a+bx+cx2 for a small disturbance from the equilibrium position.

Homework Statement Construct the analytic mapping \phi(x,y) for the H^{2+} \times S^1 representation of SL(2;R) Homework Equations g(x) \circ g(y) = g(\phi(x,y)) The Attempt at a Solution So, all points in SL(2;R) lie on the manifold H^{2+} \times S^1. I also know that SL(2;R) is...

Are there any simple elements out there that expose quadratic behavior? I. e. current to voltage or frequency to voltage or anything. I have done some google digging for multiplying circuits and found out that they are all very complex. But a simple circuit can be made using square function...