Classifying Polynomials
How do we classify(name) polynomials?
By their degree and the number of terms
Even functions are symmetric about the
Y-axis
Translate the following
As x --> - ∞, y --> - ∞,
As x approaches negative infinity, y approaches negative infinity
Odd functions are symmetric about a specific point, which we call the
origin
4x2 + 4x - 11
Classify the polynomial
7x3 - 10x5 - 1
Quintic Trinomial
Determine if the following function is even, odd, or neither.
f(x) = - x3 - 10x + 1
Neither
What is the end behavior of p(x) = x2 - x + 10
As x --> - ∞, y --> ∞,
As x --> ∞, y --> ∞
How can we determine whether a function is even, odd, or neither algebraically?
Plug in negative x for all x
What effect does h have in
f(x) = a(x -h)2 + k?
Horizontal translation
Classify the polynomial.
g(x) = -5x9 + 10x4
9th degree binomial
Slide 1
Even
Slide 2
Odd degree, negative leading coefficient
What is the degree of the following polynomial?
g(x) = 11x2 - 5x4 + 5(x3 + x4) - 1
Degree 3
( 6 - i)( 6 + i)
37
Classify the following polynomial
g(x) = -4x2 - 10 + 5 - 2(-2x2)
Constant monomial
Determine if the following is even, odd, or neither
S(x) = x9 - x3 + x
Odd
Describe the end behavior of the following function.
S(x) = -6x7 - 10x4 - 1
As x --> - ∞, y --> ∞,
As x --> ∞, y --> - ∞,
If the degree of the function is even, the arrows will point in ______ directions, if it is odd, the arrows will point in _____ directions.
(Different or The same)
f the degree of the function is even, the arrows will point in THE SAME directions, if it is odd, the arrows will point in DIFFERENT directions.
What are the three ways to solve quadratics?
Factoring, Completing the Square, and Quadratic Formula
Graphing
Classify the polynomial
L(x)= x3 - (x2 + 3x + x3) - 7x5
Quintic Trinomial
-7x5 - x2 + 3x
Even, odd, or neither
p(x) = 6x16 - 10x6 - 3
Even
Describe the end behavior of g(x).
g(x) = 2x - 6x9 + 20 - 5x
As x --> - ∞, y --> ∞,
As x --> ∞, y --> - ∞,
Even Odd or Neither
p(x) = 3x - 10 + 5x2
Neither
Identify the transformations
f(x) = -5(x - 7)2 - 10
Reflection across x-axis, Vertical stretch by 5, Shift Right 7 units, Shift Down 10