Graphs of Polynomial Functions, Graphing Polynomial Functions - End Behavior, Polynomial Graphs
same
Even degree graphs have the _____ end behavior
down
Negative leading coefficient graphs go ___ to the right.
opposite
Odd degree graphs have the ____ end behavior
Zeros
The solutions/x-intercepts on a graph
Cubic
Degree 3
f(x) = (x+1)(x-1)
-1, 1
standard form of a polynomial
terms are arranged from the largest exponent to the smallest exponent
degree of a polynomial
the greatest degree(exponent/power) of any term in the polynomial
f(x) = -(x+1)²
-1 multiplicity 2
f(x) = -(x+1)²(x-1)²
-1 multiplicity 2, 1 multiplicity 2
f(x) = -(x+1)(x-2)²
-1, 2 multiplicity 2
f(x) = x²(x+2)²
-2 multiplicity 2, 0 multiplicity 2
f(x) = -x²(x+2)(x-1)
-2, 0 multiplicity 2, 1
f(x) = x²(x+2)(x-2)
-2, 0 multiplicity 2, 2
f(x) = x(x+2)(x-1)²
-2, 0, 1 multiplicity 2
f(x) = -x²(x-2)
0 multiplicity 2, 2
f(x) = x²(x-3)
0 multiplicity 2, 3
f(x) = -x(x+1)²(x-2)
0, -1 multiplicity 2, 2
f(x) = -(x-1)²
1 multiplicity 2
monomial
1 term
binomial
2 terms
trinomial
3 terms
Down/Down
Describe the end behavior of the following equation.
Down/Up
Describe the end behavior of the following equation.
Up/Down
Describe the end behavior of the following equation.
Up/Up
Describe the end behavior of the following equation.
leading coefficient
coefficient of the first term when the polynomial is in standard form
up
Positive leading coefficient graphs go ___ to the right.
cross
What is the behavior of a multiplicity 1 zero?
bounce
What is the behavior of a multiplicity 2 zero?
two turns
What is the behavior of a multiplicity 3 zero?
Turning Points
Where the graph changes directions
Y-Intercept
Where the graph crosses the y-axis
quadratic
a polynomial with a degree of 2
constant
a polynomial with a degree of zero; for example, 5
