End Behavior
What determines the end behavior of a polynomial function
the leading term
How do you identify if a polynomial has a degree of 2?
a. It must cross the x-axis twice
b. Its graph must be a parabola
c. It must have exactly two terms
d. It must have real roots
b
Which of the following represents a polynomial with a double root at x = 2?
a. (x+2)(x-2)
b. (x-2)(x+3)
c. (x+2)2
d. (x-2)2
d
If a polynomial has roots at x=−2, x=−2, , and x=3, what is the correct factored form?
a. (x+2)2(x−3)
b. (x+2)(x+2)(x−3)
c. (x−2)2(x−3)
d. (x+2)(x−3)2
b
Which football team is Ms. Hannaberrys favorite?
The Steelers
In the polynomial f(x)=2x5−3x3+4x which term determines the end behavior?
the leading term 2x 5
A polynomial has roots at -2, 1, and 3. If the leading coefficient is 2, what is the degree of the polynomial?
3
Which statement is true about the x-intercepts of a polynomial functions?
a. They must be rational numbers
b. They represent where the function crosses the y-axis
c. They are the same as the zeros of the function
d. They can only be positive numbers
c
What is the multiplicity of the root x=2 in the polynomial f(x)=(x−2)3(x+1))?
3
How many years had Ms. Hannaberry taught for?
2
Describe the end behavior of a polynomial function with an odd degree and a positive leading coefficient?
as x -> oo y->oo and as x->-oo y->-oo
If a polynomial function has degree 6, how many turning points could it have?
at most 5
Which of the following is a root of the polynomial f(x)=x2−5x+6
A) x=1
B) x=2
C) x=3
D) Both B and C
D
If a polynomial f(x)=a(x−2)(x+3) passes through the point (1,6) what is the value of a?
-3/2
Where did Ms. Hannaberry grow up?
Long Island
If a polynomial has degree 5 and a negative leading coefficient, what is its end behavior?
as x->oo y->-oo as x->-oo y->oo
Which polynomial function represents a graph that is symmetric about the origin?
a. f(x)=x3−3x
b. f(x)=x4−x2
c. f(x)=x2+1
d. f(x)=x4+x
a
Which expression represents the factored form of x3+6x2+11x+6?
(x+1)(x+2)(x+3)
A polynomial has degree 3 and zeros at x=−1 and x=2. If f(0)=4, find the equation of the polynomial.
f(x)=2x3−3x2−4x+4
What sport did Ms. Hannaberry play in college
Womens Lacrosse
For a polynomial with a positive leading coefficient and an odd degree, the right end of the graph will go towards ...
positive infinity
What is the minimum degree of a polynomial that crosses the x-axis twice and then touches it once?
4
Given that (x−3) is a factor of P(x), what must be true?
a. 3 is the only zero of P(x)
b. P(3)=0
c. P(x) must be of degree 1
d. P(−3)=0
b
What did Ms. Hannaberry's first job?
working at a pizzeria