check my precalc

posted by .

#1. Make up a polynomial that has the following characteristics:
crosses the x axis at 1 and 4, touches the x axis at 0 ad 2. and is above the xaxis between 0 and 2.

I did (x+1)(x-4)(x^2)(x-2)^2

#2. its an illustration but one of the queestino says what is the minimum degree of polynomial. How do I find that and how do I find the maximum nuber of turnin points. I know it has to do with n-1 but Idont know how.

Thanks!!

  • check my precalc -

    should be (x-1)(x-4) to cross at 1 and 4
    should be x^2 and (x-2)^2 to touch at 0 and 2

    The last part confuses me. Since it crosses at x=1, how can it be positive for 0<x<2?

    Or, on the other hand, since it crosses at x=1, it must be positive somewhere between 0 and 2.

    Or, assuming your (x+1) factor is correct, then it shopuld have crossed at -1, not 1, and we have to consider how to make it positive for 0<x<2.

    So, since we have

    (x+1) x^2 (x-2)^2 (x-4)
    for 0<x<2, all the factors except (x-4) are positive. So, try

    -(x+1) x^2 (x-2)^2 (x-4)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. graphing exponential function

    P(x) = -(x-a)^4 (x-b)^3 (x-c) where a>0, b<0, c>0, a<c How do I sketch a graph of this?
  2. algebra

    could you help me with the following,I don't understand. Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 1.f(x) = (x + 1)(x - …
  3. polynomial functioms-check

    Can you please check my work and answers. Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 1.f(x) = (x + 1)(x - 3)(x - 1)^2 -I …
  4. Algebra help!

    I don't understand my problems that I am suppose to do. please help. Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible. …
  5. ap algebra

    can you check my answers please? Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. f(x) = 2(x - 2)(x
  6. Algebra-check my answers

    can you check my answers please? Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. f(x) = 2(x - 2)(x
  7. Writing equation of a polynomial function

    Can you help me with the following questions, I don't understand. thanks! Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small …
  8. algebra

    HELP!!!!!!!!!!!!! write equation of a polynomial function with the given characteristics. Leading coefficient is 1 or -1 crosses the x axis at -2,3, and 4 touches the x axis at 0 lies above the x axis between -2 and 0
  9. Algebra

    Do I have this right? A first degree polynomial crosses the x axis A second degree polynomial touches the y axis without crosisng A third degree polynomial flattens against the y axis.
  10. college algebra

    find the zero's for the following polynomial and give the multiplicity for each zero. For each zero, state whether the graph crosses the x-axis or touches the x-axis and turns around. f(x)=5(x-2)(x+4)^3 I am having trouble with this. …

More Similar Questions