Writing equation of a polynomial function

posted by .

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 as possible.

#1. Crosses the x-axis at -4, 0, and 1; lies above the x-axis between -4 and 0; lies below the x-axis between 0 and 1.

#2.Touches the x-axis at 0 and crosses the x-axis at 4; lies below the x-axis between 0 and 4

  • Writing equation of a polynomial function -

    for #1

    x-intercepts of a function are solutions to the corresponding equation

    since there are solutions of -4,0,and 1

    the function must have been f(x) = (x+4)x-0)(x-1)
    or
    f(x) = x(x-1)(x+4) . You can expand it or leave it as is

    for #2

    if a graph "touches" the x-axis then there must have been a double root, such as (x-2)(x-2)

    so this one clearly must have been

    f(x) = (x-0)(x-0)(x-4)
    = x^2(x-4)

    In both cases we need a cubic for 3 roots. If the x^3 is positive, then the cubic "rises" into the first quadrant and "drops" into the third quadrant.
    Since this was the case for both functions there would be a +1 understood in front of the factors,
    had it been reversed, a -1 in front of the factors would have achieved this

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Polynomial Function

    Could you help me with the following problem, I don't understand how to do it. Find an nth degree polynomial function with real coefficients satisfying the given conditions. 1. n=3; 3 and i are zeros; f(2)=20
  2. 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. …
  3. 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
  4. Precalculus

    I'm sorry I'm posting so many questions, I promise this is the last one tonight :) The leading coefficient of a cubic polynomial P is 2, and the coefficient of the linear term is -5. If P(0)=7 and P(2)=21, find P(3). I DO NOT understand …
  5. algebra 2

    Write a polynomial function that has the zeros 2, -2, and -1 and has a leading coefficient of 1. Then graph the function to show that 2, -2, and -1 are solutions.
  6. Math

    1. Identify the degree, leading term and leading coefficient of each polynomial function. A. f(x)= x(x+1)(3x+1)(x-2) B. f(x)= -16+3x^4 - 9x^2 - x^6 + 4x^8 2. Describe the end behavior of a ninth-degree polynomial function with a negative …
  7. Math

    Write a polynomial function in standard form that has the given zeros and has a leading coefficient of 1 for: -2, 4+i
  8. Math

    Determine whether the following statement makes sense or does not make sense, and explain your reasoning: When I'm trying to determine end behavior, it's the coefficient of the leading term of a polynomial function that I should inspect. …
  9. poloynomial function

    Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. 1) -2, -1, 1 2) i, 4 3) i, 2 - √3 4) 1, 4, 1 + √2
  10. algebra

    A cubic polynomial function f(x) has leading coefficient -2 and intercepts the y-axis at 2. If f(1)=1, and f(-2)=-2, find f(-1) and write the complete function.

More Similar Questions