1. V


    Hello, I need to solve the following. Ax^2+By^2+Cxy=0 I suppose I have to make some substitution, but I have no idea how! Thanks for any help Vale
  2. C

    Suppose that ax+y=b and that ax^2+y^2=b^2. What are the possible value(s) of y?

    Options: 1) b * 1+a/1-a 2) -b 3) b * 1-a/1+a 4) (b-b(sqrt(1-4/a)))/2 5) ab - b 6) b/a 7) -b/a 8) b - ab 9) b 10) (b+b(sqrt(1-4/a)))/2 PLEASE HELP ME! Thank you in advance.
  3. Matt Westwood

    Primitive of (ax^2 + bx + c)^(n + 1/2)

    No. 295 in my list of difficult integrals ... Integral of the general power of a x^2 + b x + c: the object here is to establish the following reduction formula: \int \left({a x^2 + b x + c}\right)^{n + \frac 1 2} \ \mathrm d x = \frac {\left({2 a x + b}\right) \left({a x^2 + b x + c}\right)^{n...
  4. Matt Westwood

    Integral of x^2 sqrt (ax^2 + b x + c) dx

    Integral number 287 is similar to 286: \int x^2 \sqrt {ax^2 + b x + c} \ \mathrm d x I haven't found a useful substitution: z = x^2, \frac 1 u and \sqrt {ax^2 + b x + c} all seem to lead nowhere. I have also tried splitting it into u = x, \mathrm d v = x \sqrt {ax^2 + b x + c} but the algebra...
  5. Matt Westwood

    Integral of x sqrt (ax^2 + b x + c) dx

    We're up to number 286 in Fiendish Integrals for Masochists ... \int x \sqrt{a x^2 + b x + c} \ \mathrm d x The posted solution is: \frac {\left({\sqrt {a x^2 + b x + c} }\right)^3} {3 a} - \frac {b \left({2 a x + b}\right) \sqrt {a x^2 + b x + c} } {8 a^2} - \frac {b \left({4 a c -...
  6. Matt Westwood

    Integral of 1 / (x sqrt (ax^2 + b x + c)) dx

    I'm working my way through a series of ever tougher integrals. I'm stuck at no. 283: \int \frac {dx} {x \sqrt {a x^2 + b x + c} } ... and there are some further even tougher ones. I understand that it is supposed to evaluate to: - \frac 1 {\sqrt c} \ln \left({\frac {2 \sqrt c \sqrt {a x^2 +...
  7. A

    Find the cubic function y = x3 + ax2 + bx + c

    Find the cubic function y = x^3 + ax^2 + b^x + c whose graph has a horizontal tangent at (-2, 10) and passes through (1,1). What I tried so far is plugging in -2 and 1 in the original function to get: -8 +4a -2b +c = 10 1 + a + b + c = 1 And I have y' = 3x^2 + 2ax + b, which when I plug in -2 I...
  8. H

    M = max|f(x)|≥1/4 where f(x) = x^3+ ax^2+ bx +

    Let f(x) = x^3+ ax^2+ bx + c with a, b, c real. Show that M = max|f(x)|≥1/4 -1 ≤ x ≤ 1 and find all cases where equality occurs. so far i have Let h(x)=x^3, then let g(x)=mx, we need to find m so that g(x) can get as close to h(X) with an even minimum distance between them, between [-1,1] By...
  9. M

    please help!! x^3 + ax^2 + bx+ c

    Hi so I am a student of Maths and Physics Track in my school And in todays class in Maths, the teacher gave us a question. And when no one could solve it, he said that there is going to be a quiz in it tomorrow I tried to solve it several times but I couldn't solve it anyways,, the question...
  10. J

    Quadratic Functions Question - Find in Form of y = ax2 + bx + c

    Hey All Got a test tomorrow, I'd appreciate some help. I'm pretty good in math but I just don't get these questions here. Find, in the form y = ax2 + bx + c, the equation of the quadratic whose graph: q1) touches the x-axis at 4 and passes through (2,12) q2) has vertex (-4, 1) and...
  11. D

    Quadratic Equations of the form Ax^2 + BX + C

    I am trying to get to understand this subject but can't seem to grasp it from the books? I have; y = X^2 + 2x - 3. This is what I have tried so far; (x + 2) (x - 1.5) x = - 2 or x = 1.5 - 2 + 1.5 = - 0.25 2 y = - 0.25^2 + 2 ( -0.25) - 3 ( -4, -1) I know it's wrong but can't...
  12. K

    Finding a and b, of ax^2 + bx + c, when given an equation of the tangent line

    Hey! I didn't really know what to put as a title so I hope it describes the problem relatively well... I have been working on this problem for about 20 minutes and haven't come very far, so I was hoping for someones help in putting me in the right direction! Question For what values of a and b...
  13. L

    Quadratic Equation Hidden, ax^2+bx+c=0

    Hey all, I need help with this equation. It is a hidden equation which I have tried to solve on my maths booklet. The steps that must be followed are: ax^2 + bx + c = 0 I have to use the quadratic formula and tranpose the above here is my question 1 / R + R = 3 + 7 / R I need to get the...
  14. A

    Regression for Ax^2+Bx+C

    Hi there, I have a set of data points {(X1,Y1), (X2,Y2),........(Xn,Yn)} I would like to approximate the relation between X and Y as a parabola. Assuming the parabola has form y = Ax^2+Bx+C, can somebody please provide me with the least squares regression formulas for A, B and C. Any help...
  15. planolerachel

    factoring trimonials of the form ax^2+bx+c where a does not equal 1

    I am in need of some help... I can't seem to figure out this problem... factor completely 2u^2 + 5uv +3v^2 any help is much appreciated.
  16. N

    What values of a makes f(x)= ax^2 + (a+1)/x have a horizontal asymptote when x->+/-∞?

    If you could explain how to do this I would be SOOOO grateful! Thanks!!! I have no idea where to start...
  17. M

    Complete the square of ax^2+bx+c where b=0

    I'm sure the method is just slipping my mind, and I've done this before, but only once since I cannot find an example in my book. The question is stated like this. The path of a basketball shot can be modelled by the equation h=-0.125d^2+2.5, where h is the height of the basketball, in meters...
  18. P

    For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 wh

    __a=1/2 __b=-8 __a=-1/2 __b=8 __a=-20