Polynomial Basics
Roots
Polynomial Graphs
2.6 & 2.7 💀
Miscellaneous
100
True or false. f(x)=3x+1 is a polynomial.
True
100
"Roots" is a word that is used to describe what about a polynomial?
Zeros or x-intercepts
100
What word is used to describe the shape of a quadratic function?
Parabola
100
This function has one vertical asymptote. State it's equation. f(x)=1/(x+2)
x=-2
100
True or false: Constant functions are NOT polynomials.
False
200
What term is used to classify the polynomial based on the highest powered term?
Degree
200
According to the Fundamental Theorem of Algebra, how many complex roots will f(x)=x^4 + 2x^5 + 3x^6 + 4x^7 have?
7
200
Polynomials whose end behavior goes to opposite directions on either side have an ____ degree.
Odd
200
How many total asymptotes does g(x)=x/(x^2-1) have?
3:
x=-1, x=1, y=0
200
How many times will a polynomial graph with no real solutions cross the x-axis?
None
300
In the polynomial 4x^2 + 3x-1, 4 is considered the...
Leading coefficient
300
Write down all zeros of the polynomial f(x)=(x+10)(x-2)(x^2 + 1).
-10, 2, +-i
300
How old is Mr. Kriss?
27
300
A polynomial with 3 real zeros will have how many intervals that you need to test?
4 intervals
300
The point at which a polynomial switches from a increasing slope to a decreasing slope.
Point of inflection
400
Write down a fifth degree polynomial with two terms that has the following end behavior:
lim_(x->-infty)f(x)=infty
lim_(x->infty)f(x)=-infty
Example:
f(x)=-x^5 + 1
400
A fourth degree polynomial is graphed below. How many real zeros and complex zeros does it have?
2 real, 2 complex
400
Draw a 3rd degree polynomial with zeros -2, 1, and 4 with the end behavior: lim_(x->-infty)f(x)=-infty, lim_(x->infty)f(x)=infty.
400
When solving a polynomial inequality like f(x)>=0 , the second step is to set f(x) equal to 0 and solve. Those solutions are called ________________.
Boundary points
400
If a complex number a+bi is a solution to a polynomial function, then what must also be another known solution?
a-bi
500
Write down the general form of a polynomial of degree n with coefficients a_n, a_(n-1),..., a_2, a_1, a_0.
f(x)=a_nx^n + a_(n-1)x^(n-1) + ... + a_2x^2 + a_1x + a_0
500
Write down all zeros of f(x)=x^4 + 4x^3 + 16x^2 + 64x.
x=-4, 0, +-4i
500
Draw a polynomial graph that could match the function f(x)=(x+1)^2(x-1)^3.
500
Solve x^3-x<=0.
(-infty,-1]cup[0,1]
500
State the multiplicity of the smallest real root in the polynomial f(x)=(x-3)^2(x+1)^4(x+2)^3.
3