Naming Polynomials
Write the following polynomial in standard form and name it:
3x2 - 7x4 + 9 - x4
What is:
-8x4+3x2+9
Quartic Trinomial
Identify BOTH the domain and range of the following polynomial:
5x4 -2x2 - 1
What is:
Domain: ( -infinity, +infinity )
Range: [ -1.2, +infinity )
The arrows at the ends of a positive quadratic binomial go in these directions:
Left?
Right?
*by the way...this is not really end behavior*
What is:
Left: UP
Right: UP
What is:
touch or cross the x-axis
Sketch a graph of the following polynomial with the solutions clearly identified:
y = -7x6 +7x3
Negative Even graph with solutions marked at X=0, x=1
Write the following polynomial in standard form and name it:
5x2 - 9x5 + 8x3 - 11
What is:
-9x5+8x3+5x2 - 11
Quintic Polynomial with four terms
Identify BOTH the domain and range of the following polynomial:
- 2x4 - x3 +2x2 + 1
What is:
Domain: ( -infinity, +infinity )
Range: ( -infinity, 2 ]
LEFT: As x ---> -infinity, y ---> -infinity
RIGHT: As x ---> +infinity, y ---> -infinity
The leading coefficient and highest degree are __________ ?
What are:
NEGATIVE & EVEN
What are the solutions to the following polynomial:
y = 2x4 + 3x - 5
x = -1.473
x = 1
Sketch a graph of the following polynomial with the solutions clearly identified:
f(x) = -x7 - 1
Negative Odd graph with solution marked at X=-1
Write the following polynomial in standard form and name it:
5x3 - 6x3 + 8x2 - 10 + x - 8x2 - x
What is:
-x3 - 10
Cubic Binomial
Identify BOTH the domain and range of the following polynomial:
6x3 - 2x2 - x
What is:
Domain: ( -infinity, +infinity )
Range: ( -infinity, +infinity )
LEFT: As x ---> -infinity, y ---> -infinity
RIGHT: As x ---> +infinity, y ---> +infinity
The leading coefficient and highest degree are __________ ?
What are:
POSITIVE & ODD
What are the solutions to the following polynomial:
f(x) = 4x3 + 3x2 + 2
X = -1.137
Sketch a graph of the following polynomial with the solutions clearly identified:
y = 2x3 - 5x2
Positive Odd graph with solutions at x=0 & x = 2.5
Write the following polynomial in standard form and name it:
(x + 4)(x - 3)
*hint use the box method*
What is:
-x2 + x - 12
Quadratic Trinomial
Identify BOTH the domain and range of the following polynomial:
-6x3 +2x2 + 3x
What is:
Domain: ( -infinity, +infinity )
Range: ( -infinity, +infinity )
Write out the end behavior for the polynomial below:
f(x) = x4 + 3x2
What is:
LEFT: As x ---> -infinity, y ---> +infinity
RIGHT: As x ---> +infinity, y ---> +infinity
A negative cubic polynomial with six terms can have 0, 1, 2, or 3 solutions...true of false.
What is:
FALSE
*Any type of cubic polynomial always has at least ONE solution*
Sketch a graph of the following polynomial with the solutions clearly identified:
y = -10x5
Negative Odd graph with solution at x=0
Rank the following in order least to greatest:
linear, quintic, quadratic, constant, cubic, quartic
What is
constant, linear, quadratic, cubic, quartic, quintic
Which equation below has a RANGE of:
[ -2.5 , +infinity )
A) 12x4 - 6x2 + 2
B) 5x2 - x + 1
C) 2x4 + 3x3 - 4x - 1
D) 13x3 - 2x2 + x - 19
What is:
2x4 + 3x3 - 4x - 1
Write out the end behavior for the polynomial below:
f(x) = -x3 + 3x2 + x - 122
What is:
LEFT: As x ---> -infinity, y ---> +infinity
RIGHT: As x ---> +infinity, y ---> -infinity
What are the solutions for the following polynomial:
3k2 - 18k - 21
(solve by factoring)
What are:
X = -1
X = 7
Create a polynomial with a graph that has exactly 4 solutions. Sketch a picture of the graph and write out the polynomial with its proper name included.
*answers may vary