calculus

given the following function find,

a. zeros and the multiplicity of each
b. number of turning points
c. end behavior

f(x)=(x-1)(x-5)
a. x=1 and x=5--is this correct?

b. number of turning points
I had f(x)-0 BUT my teacher said this--
Note that the equation has a degree of 2. f(x)=x^2-6x+5. How many turning points must an equation have that is of degree two? Is it two points--(1,0)and (5,0)

c. end behavior
I had for a large |x|(positiveor negative) f(x) increases as parabola upward to infinity BUT my teacher said not to change to an absolute value. Can someone help me with this one.
**please show work**

  1. 👍 0
  2. 👎 0
  3. 👁 67
  1. Your function is a simple parabola
    All parabolas have one turning point, called the vertex

    because of the + understood in front of
    f(x) = +x^2 ....
    the parabola opens upwards so it rises to infinity in both the 1st and 2nd quadrants.
    If the function had been
    f(x) = -x^2 .... , then it would have opened downwards. Your teacher was right to object to the |x| , that would always make the sign in front a +

    Your zeros of x=1 and x=5 are correct, their multiplicity is 1

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra

    Please help. Having a hard time with this. Find all of the zeros of the polynomial function and state the multiplicity of each. f (x) = (x^2 – 16)^2 A. – 4 with multiplicity 2 and 4 with multiplicity 2 B. – 4i with

    asked by Britney on July 22, 2009
  2. Algebra

    Find all of the zeros of the polynomial function and state the multiplicity of each. f (x) = (x^2 – 16)^2 A. – 4 with multiplicity 2 and 4 with multiplicity 2 B. – 4i with multiplicity 2 and 4i with multiplicity 2 C. 4 with

    asked by Audrey on July 23, 2009
  3. Algebra

    Find all of the zeros of the polynomial function and state the multiplicity of each. f (x) = (x^2 – 16)^2 A. – 4 with multiplicity 2 and 4 with multiplicity 2 B. – 4i with multiplicity 2 and 4i with multiplicity 2 C. 4 with

    asked by Breanna on July 20, 2009
  4. calculus-can someone please help me with this ques

    Given the following polynomial find, a. zeros and the multiplicity of each b. number of turning points c. end behavior f(x)=(x-1)(x-5) a. the multiplicity of (x-1)(x-5) x=1 and x=5----is this correct b. number of turning points I

    asked by Jimmy-can someone please help on December 18, 2012
  5. calculus

    Using a graphing utility, graph and approximate the zeros and their multiplicity. A.x=0,multiplicity 2;x=7,multiplicity 3 B. x=0,multiplicity 2; x=7,multiplicity 1; x=-7, multiplicity 2 C. x=0,multiplicity 3;x=0,multiplicity 2

    asked by CC on September 20, 2010
  6. Algebra

    Find all of the zeros of the polynomial function and state the multiplicity of each. f (x) = (x^2 – 16)^2 – 4 with multiplicity 2 and 4 with multiplicity 2 I think this is the ans for this equation. Anyone care to chime in?

    asked by Angie on July 24, 2009
  7. Math

    I just wanted to double check that I am correct. 1.Find the zeros for the function: f(x)= 4(x-3)(x+2)(x-4)^2 Zeros are: 3,-2, 4(multiplicity 2) 2.Find the zeros for the function: f(x)= x^3-9x Zeros are: 0, 3, -3

    asked by kim on October 17, 2014
  8. calculus-can someone please help me with this ques

    Given the following polynomial f(x)=(x-1)(x-5), find A.the zeros and the multiplicity of each one b. where the graph crosses or touches the x-axis c.the number of turning points d. the end behavior Please show work.

    asked by Ladybug--Please help!!!! on December 17, 2012
  9. pre calculus

    Given the following polynomial; f(x)=(x-2)^3 Find: a. the zeros and the multiplicity of each b. where the graph crosses or touches the x-axis c. number of turning points d. end behavior I have no clue what I am doing. pleeeaaase

    asked by sally on April 10, 2013
  10. 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 -

    asked by Tyra on October 20, 2007

More Similar Questions