The graph of polynomial function f(x)=a(x+1)^2(x−2) passes through point (0,2). Find the value of a.

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A:

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A: We know that a third-degree polynomial with a negative leading coefficient when used to model…

Q: Determine an equation in fortored form for a polynomial function with zeros x=-3 (order 2) and x = 2…

A: We have to determine an equation in factored form for a polynomial function with zeros: x=-3 order 2…

Q: sketch the polynomial function by finding all critical values. f(x)=x4-x3-20x2

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Q: A polynomial function with leading term 2x to the power of 3 has a degree

A: We know that a polynomial with highest degree is the leading term.

Q: find an equation for a polynomial with long run behavior g(x)=-x^4 whose only intercepts are (-5,0),…

A: intercepts are  (-5, 0) , (5, 0) , (2, 0) and (0, 2)  g(x) has degree of 4    Let,  g(x)  =  ax4 +…

Q: Sketch the graph of the function by (a) applying the Leading Coefficient Test, (b) finding the real…

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A: suppose, we have a polynomial function, y=-2x-2x2+1

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A: Given,           y'=x+y2 if y(0)=2

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A:

Q: Find a degree 3 polynomial having zeros -2, 1 and 8 and the coefficient of x3x3 equal 1. The…

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Q: Sketch the graph of a fifth-degree polynomial function whose leading coefficient is positive and…

A: Consider the provided information, The zeros at x=3 of multiplicity 2. That is x-32 The standard…

Q: Is it possible for a polynomial to have two local maxima and no local minimum? Explain.

A: Maxima and minima: Functions make hills and valleys when they reach a minimum or maximum value in…

Q: What is a polynomial function?

A: To Explain: what is a polynomial function

Q: A herd of 100 elk is introduced to a small island. The number of elk, f(x), after x years is modeled…

A: Here given polynomial function as fx=-x4+21x2+100 or it can be written as fx=-x22+21x2+100 Thus it…

Q: How do I find a polynomial function with given zeros and multiplicities?

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Q: A 4th degree polynomial has zeros -5, 3, i, and -i. Which could represent the function defined by…

A: here it is given that A 4th degree polynomial has zeros -5,3, i and -i

Q: Why is a third-degree polynomial function with a negative leading coefficient not appropriate for…

A: Note that a third-degree polynomial with a negative leading coefficient that used to model real-life…

Q: find a polynomial of degree 4 with zeros -6,-1,0, and 3.

A:

Q: Determine a possible 3rd degree polynomial function in factored form with its only (3, 0) and (-2,…

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Q: Determine whether the statement is true or false, "Every polynomial equation of degree 3 with real…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Sketch the graph of the function by (a) applying the Leading Coefficient Test, (b) finding the real…

A:

Q: Explain how to use the Leading Coefficient Test to determine the end behavior of a polynomial…

A: case (1) When n is odd and an  is positive. Then the graph is falls to the left and rises to the…

Q: write a polynomial function of minimum degree in standard form with real coefficients whose zeros…

A: For any polynomial having roots (a,bc,d) We can write polynomial as (x-a)(x-b)(x-c)(x-d)

Q: Find the formula for the fourth degree polynomial containing the point (0,8) and whose graph is…

A: We have to find the equation for the given graph.

Q: 20. Explain how instantaneous rates of change could be used to locate the local maxima and local…

A: Given

Q: What are the zeros of a polynomial function and how are they found?

A: Let f(x)=anxn+an-1xn-1+⋯+a3x3+a2x2+a1x+a0  be a polynomial of degree n. A root or a zero of a…

Q: Find the x-intercepts of the polynomial function. f(x) = x3 – 3x2 - x + 3 (x, f(x)) : |(smallest…

A: f(x)=x3-3x2-x+3

Q: What is meant by the end behavior of a polynomial function? Explain.

A:

Q: Find a polynomial function of degree three with numbers 3, 5, -2 as zeros of the polynomial.

A: Calculation:

Q: sketch the polynomial function by finding all the critical values. g(x)=x4-4x3-15x2+58x-40

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Q: How to find the cubic polynomial function that has zeros of x=2, x=3(+or -) i

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Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A: We have to find

Q: The degree of a polynomial is the highest exponent of x when in standard form. How are even degree…

A: Let's find.

Q: polynomial function with real coefficients whose zeros are as shown in the image and a solution…

A:

Q: 4. Determine a possible equation for the polynomial function that corresponds to this graph.

A: Let's Solve,

Q: write a polynomial function of minimum degree in standard form with real coefficients whose zeros…

A:

Q: find a degree 3 polynomial with zeros -2,1, and 5 and going through the point (0,-3)

A: Assume a polynomial and use the given point.

Q: Find a cubic polynomial f(x)=ax3+bx2+cx+d that has horizontal tangents at the points (-5,4) and…

A: Let the cubic polynomial function be fx=ax3+bx2+cx+d. It is given that the function f(x) has…

Q: Use the graph to identify the formula for a polynomial function of least degree. y 5- 4- 21 1+ -5 -4…

A:

Q: how do I Write a polynomial function of least degree with integral coefficients that has the given…

A: If k is a zero  of the  polynomial p(x)  then (x - k) is a factor of  p(x)

Q: The x-intercepts of the graph of a polynomial function are called turning points.

A: See attached file for a step by step explanation.

Q: The graph of a polynomial function will appear to bounce off the x-axis at zeros that are of an even…

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Q: onstruct a polynomial function with the following properties: fifth degree, 4 is a zero of…

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Q: What is the polynomial function in standard form with a root of multiplicity 1 at x= 3, and a root…

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Q: What are the maximum numbers of relative extrema and points of inflection that a fifth-degree…

A: A fifth degree polynomial is to be first differentiated first.  Now the first differentiable will be…

Q: Use the graph to identify the formula for a polynomial function of least degree. y 5- 4- 2 1+ +►X -5…

A: 1. Identify the x-intercepts from the graph In the above graph the x intercepts are at x=-4 , x=-2…

Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A: Given  zeros of polynomial x= -1 and x= 4

Q: What is a cubic polynomial function in standard form with zeros -4, -5, and 4?

A: