Quadratic Definition and 990 Threads

[SOLVED] Quadratic Equations and Inequalities question about properties of quadratic so here is the question graph the function. state the domain and range of the function. F(x)=-2x^2-3x+2 i try and use the axis of symmetry (-b/2a) and then plug that into the original formula to get the...

Homework Statement Given that the roots of x^2+px+q=0 are \alpha and \beta, form an equation whose roots are \frac{1}{\alpha} and \frac{1}{\beta} b) Given that \alpha is a root of the equation x^2=2x-3 show that i)\alpha^3=\alpha-6 ii)\alpha^2-2\alpha^3=9Homework Equations...

Q: Suppose q(X)=(X^T)AX where A is symmetric. Prove that if all eigenvalues of A are positive, then q is positive definite (i.e. q(X)>0 for all X not =0). Proof: Since A is symmetric, by principal axis theorem, there exists an orthogonal matrix P such that (P^T)AP=diag{c1,c2,...,cn} is...

I have a bouncing ball quadratic equation and know that B represents the initial velocity. My question is why does B the initial velocity increase with each bounce of the ball. It seems paradoxical to me, particularly if total energy is decreasing. y=ax^2 + bx + C I have attached...

Homework Statement "Tell whether the statement is true and give a counterexample if it is false" "Let m > 0 and (m, ab) = 1. If neither x^2 congruent to a (mod m) nor y^2 congruent to b (mod m) is solvable, then z^2 congruent to ab (mod m) is solveable. Homework Equations Legendre...

Arc Length, Irreducible quadratic factors i'm having a hard time seeing this method, and i have to use this method on one of the problems I'm doing to find it's Arc Length. L=\int_{\sqrt{2}}^{\sqrt{1+e^{2}}}\frac{v^{2}dv}{v^{2}-1}} the book suggests to first divide then use a...

[SOLVED] Help on tis quadratic functions question Homework Statement The speed v m/s of a particle traveling from A to B at time t s after leaving A, is given by v =10t-t². the particle starts from rest at A and comes to rest at B. Show that the particle has a speed of 5m/s or greater for...

Homework Statement I am trying to use the quadratic formula for 3x^2 - 12x +11 and I am getting... 12 +/- (sqrt 12)/6 which is supposed to reduce to 6 +/- (sqrt 3)/3 and I can't figure it out...it's very sad!

Ax^2+Bx+C=0 PROGRAM delta1 IMPLICIT NONE REAL :: A,B,C REAL :: DELTA,X1,X2 PRINT *,"Enter the a,b,and c" READ *,A,B,C delta=b**2-4*a*c IF (delta>0)THEN PRINT *,"The roots are real" X1=(-B+SQRT(DELTA))/(2*A) X2=(-B-SQRT(DELTA))/(2*A) PRINT *,"X1 = ",X1,"X2 = ",X2...

can i always the quadratic forumula when i m doing these types of problems. my teacher said i can but sometimes theirs faster ways to do it

Homework Statement Hello everyone! How would you solve a quadratic or nth degree congruence? For example how would I solve: (x^2) + 2x -3 = 0 (mod 8 ) The Attempt at a Solution I know this can be written like: (x^2) + 2x = 3 (mod 8 ) but where would I go from here? and...

Hi, I need to extrapolate vector v_{-1} from v_{0}, v_{1} and v_{2} (see attached pic), so that if v_{2} is on the right/left (2D case for simplicity) of v_{1}-v_{0}, v_{-1} would also be on the right/left. My initial solution was like this: v_{2} - v_{1} = v_{1} - v_{0} + dv, v_{1} - v_{0}...

I have to write the equation of motion for a projectile thrown vertically, under quadratic air resistance. The forces acting on the projectile then are, gravity and the quadratic air resistance. Now, both forces are opposing the projectile, would that mean that if I make gravity negative...

Homework Statement basically I am suppose to linearize d=vit + 1/2at^2 into d/t^2 vs 1/t, t/d vs t^2/d and 1/d vs 1/t and its asking which graphs would be linear and non-linear. Homework Equations d=vit + 1/2at^2 The Attempt at a Solution all i know is that in order to linearize this i...

Homework Statement Hello, I just found a question, and having attempted it many times I get different answers, probably due to my messy working, however I have just tried it twice again and got the same answer, just checking with you guys to see if you think it is correct. Thanks...

Homework Statement Suppose that an object is thrown into the air with an initial upward velocity of Vo meters per second from a height of ho meters above the ground. Homework Equations Then, t seconds later, its height (h(t) meters above the ground is modeled by the function h(t) = -4.9t^2...

Hi everyone, I need help again… on “quadratic inequality”. How come the 1/3 < |x| < 1/2 become 1/3 < x < 1/2 or 1/3 < −x < 1/2? And, this is the original problem of above solutions: 1/9 < x^2 < 1/4. I wasn’t able to find the proof from my calculus book because the book says: 1) |x| =...

This is a simple word problem that I just can't wrap my head around. The answers are 7 and 9: The sum of two numbers is 16, but the sum of their squares is 130. Find the numbers. I am supposed to use a quadratic equation as a means to solve the question, and all I need to do is to create...

Hi, How to find the equation if one root of a quadratic equation is 1 + 3i. Regards, Suganya EasyCalculation ToFocus

Homework Statement I need to find the congruence classes mod (3 + sqrt(-3))/2 in Q[sqrt(-3)]. Homework Equations None known. The Attempt at a Solution I'm not sure how to go about finding these congruence classes. I know that in the regular integers congruences classes mod x are...

Homework Statement For my number theory course, I'm supposed to come up with a definition of congruence in quadratic integers, and define the operations of addition, subtraction, and multiplication. Homework Equations None known. The Attempt at a Solution I honestly have no real...

I'm currently going through some questions and came across quadratic and linear simultaneous equations. Solve the equation: x + y = 1 x^2 + y^2 = 16 I am not interested in the question itself but rather the explanation the book gives me which says after...

Homework Statement How to find the conditions on the coefficients of a quadratic equation for the roots to be outside the unit circle eg bx^2 + x - 1 = 0 where b is a constant How do we find the condition(s) that b must satisfy such that the roots of the quadratic lie outside the unit circle...

This is about flash scripting, actually. There's that thing called quadratic bezier spline, p_0(1-t)^2+2p_1 t(1-t)+p_2 t^2, right, and flash plugin has that "curveTo" command that apparently uses above expression for x(t) and y(t) to draw a curve between two points on screen. So, I was...

Homework Statement A projectile is launched upward. Its height above the ground after t seconds is -16t^2 + 320t. After how many seconds in the air will it return to the ground? Solve algebraically. Homework Equations ax^2+bx+c=0 ? -b (+/-) (Square root of b^2 -4ac)/2a ? The...

Quadratic Question... I have no problem solving this problem. My question is about the wording. Homework Statement Find two consecutive integers whose product equals 30. Homework Equations unnecessary The Attempt at a Solution x(x+1)=30-->x^2 +x-30=0---->(x+6)(x-5)=o--->...

How does the second term in a quadratic, bx, affect the graph?

Homework Statement A physics student with too much free time drops a watermelon from the roof of a building height H. He hears the sound of the watermelon going "splat" after a time interval of Delta T. You may ignore air resistance. How high is the building? The speed of sound is Vs...

a) (i) (x-14)(2x-7) (ii) x = 14 or x = 3.5 b) i) \frac{7}{n+7} ii) Take n to be 8 \frac{7}{8+7} \frac{7}{15} that DOESN'T round down to \frac{2}{5} Is that all correct so far? If so I will post the next (really hard) question)... Thanks

Homework Statement Solve for all real x: (x^2-6x+9)^(x^2-4)=1 Homework Equations The Attempt at a Solution I raised both sides by 1/x^2-4, so got x^2-6x+9=1, solved it to get x=2,4. It's a question from a college enterance exam sample paper, so I wondered if it could be that...

Quadratic in standard form help...please Homework Statement Write the quadratic function f(x) = x^2 + 3x + 2 in standard form. Homework Equations Standard form equation : f(x) = a(x-h)^2 + kThe Attempt at a Solution Ok, I think I got this one but am wanting to be sure. I set it up : (x^2...

Homework Statement Find a quadratic function f(x), that satisfies the given conditions: f(1) = 2, f(-1) = 4, f(3) = 8. Thanks Homework Equations f(x) = k(x-s)(x-t) The Attempt at a Solution I tried entering the points as the the x and f(x) while estimating as what the...

The height h of the ball is given be h = 1.2 + 20t -5t^2, where t is in seconds. If the ball is caught at the same height at which it was hit, how long is it in the air? How do I figure out the time? quadratic function? -b/2a?

A family of quadratic functions passes through the points (3,0). Find the family of quadratic functions err i have no idea hwo to do it except substituting those values in ... 0=9a+3b+c what does it meant the family of quadratic functions?

<b>I need a brain refresher</b> to see if i have everything straight in quintic and quadratic expressions. The n's in an expression represents how many turns a line would have The amount of (x+1)^2 means a quadratic curve The if the n is odd there are no complex roots Now here is the...

Homework Statement Need to solve 2x² + 5x + 3 = 0 Homework Equations at² + bt + c = 0 so a = 2, b = 5, c = 3 The Attempt at a Solution a x c = 6 a + c = 5 so ned to find somthing that times to make 6 and add to make 5. That is 2, 3 2x² + 2x + 3x + 3 2x (x + 1) + 3(x...

1. A quadratic fraction is of the form f(x)= 2x^2+bx+5 Find the values for b where the graph of f(x): 1.just touches the x-axis 2. has two x-intercepts 3.does not cut or touch the x-axis I've tried using the quadratic formula but i have no idea how to do it when there are two unknowns...

I have been given a root of 4, a y-intercept of 12 and a known point of (2,8). I have then been asked to write the equation in the form of y=a(x^2)+bx+c I am assuming the relevant equations are: y=a(x-"alpha")(x-"beta") Ok, so I know that c=12, but I can't see how I draw the a and b part...

All, I am not sure how to handle this situation with complex numbers. Can you help? Q = A^2 + ABi Where Q is a complex number. Can we not solve for A if we know Q and Bi using a quadratic equation? 0 = A^2 + ABi + -Q Let... Q = 455 Bi = -22 And in this case I do know...

Homework Statement I have the following question to answer: Show that (X^2/h^2)*((1/2*y1) - y2 + (1/2*y3)) + (X/h)*((-1/2 y1)+(1/2 y3))+y2 (sorry about the format) is equal to (taylor expansion): y = y2+(x(dy/dx)¦0 + (x^2/2*((d^2)y)/(dx^2))¦0 Homework Equations also given in...

Hey everyone, We've been covering tangents and derivatives etc in class recently but there is a question on the assignment that we've been given that i don't know how to do. The question is: "A quadratic equation can be fitted to any three points on a cartesian plane. The model for such...

Can you please help me with this quadratic word problem? An airplane flies 520 km against the win and 680 kim with the wind in a total time of 4hr. The speed of the airplane in still air is 300kim/hr. What is the speed of the wind? Any suggestion is greatly appreciated!

Velocity using quadratic formula- NEED HELP PLEASE! Here is the problem: An osprey is flying over a reservoir with a trout in her talons. Her speed is 4.21 mph and the reservoir is 12.76 feet below. She is flying at an angle of 15.32 degrees below the horizontal- A- Calculate the...

The question is: Show that if p == 1 mod 4, then (a/p) = (-a/p). (Note that == means congruent). I know that if X^2==a mod p (p is a prime) is solvable then a is a quadratic residue of p. For an example, I let p = 5 since 5==1 mod 4. Then, I let X = 2 and 4 just to check the equation...

I might not be the brightest bob in the bunch but I am having trouble with a simple quadratic equation. k^2 + (k + 4)^2 = 346 According to my manual expands to: k^2 + k^2 + 8k + 16 = 346 Everything is going fine until I see the 8k. Where did the 8k come from? Or is my...

I am stuck on this problem. I can reach the correct answer with the quadratic formula, but not with the method suggested (completing the square). Thanks in advance. The problem is: 2x^2+8x+1=0 This is what I tried: 2x^2+8x=-1 2(x^2+4x)=-1 2(x^2+4x+4)=-1+8 2(x+2)^2=7...

i think I am pretty much 'in the know' about this one. it's an equation about a football player kicking a football.. h = -4.9t^2 + 10t + 3 h = height (in meters) t = time (in seconds) so the vertex is 9.25m height at 1.25 seconds? (i figured this on my graphing calculator). and the...

1) "find the vertex algebraically" y= -x^2 - 3 y = (x - 3)(x+1)?? (the -x is throwing me off) 2) a movie theatre sells tickets for $8.5 each. they are considering raising the prices but know that for every 50 cents the price is raised, 20 fewer people go to the movies. R = -40c^2 + 84c...

I have a huge headache and I can't understand why this works... I am reviewing the quadratic formula so that I can solve trig questions, but I am stuck on this one part... The point is to factor x^2+2x-1 I ( and the textbook ) use the quadratic formula to get the roots of it and come up...

This question has been killing me for days, : Give a family of quadratic functions of the form y=ax^2+bx+c, that passes through the following points: (1,1) and (2,0) I see how we can find the family, but how do we find the specific functions that pass through both those points? I tried making...