27. The complete graph of a polynomial function whose zeroes are integers is sho

Question

27. The complete graph of a polynomial function whose zeroes are integers is shown.
A. Find the zeroes and state whether the multiplicity of each zero is even or odd. What are the zeroes of f?
The solution set is { ?,? }
Is the multiplicity of the leftmost zero odd or even? Is the multiplicity of the rightmost zero odd or even?
B. Write an equation, expressed as the products of factors, of a polynomial function that might represent the graph shown. Use a leading coefficient of 1 or -1, and make the degree of f as small as possible.
f(x)= ?
C. Use the equation in part (b) to find the y-intercept.
y= ?
1lby 10, 50, 101

Explanation / Answer

a) the zeros of the function are points where graph cuts x axis

if graph cuts x axis it means zero has odd multiplicity

if graph touches x axis it means the zero has even multiplicity

at x = -2 graph crosses x axis , hence it is odd multiplicity

at x = 4 graph touches x axis , hence it is even multiplicity

b) the polynomial can be expressed as

f(x) = 1 (x-a ) (x-b)

where a , b are zeros of the function

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

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.