The degree of a polynomial function helps us to determine the number of
x -intercepts and the number of turning points. A polynomial function of
$\text{\hspace{0.17em}}n\text{th}\text{\hspace{0.17em}}$ degree is the product of
$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ factors, so it will have at most
$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ roots or zeros, or
x -intercepts. The graph of the polynomial function of degree
$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ must have at most
$\text{\hspace{0.17em}}n\u20131\text{\hspace{0.17em}}$ turning points. This means the graph has at most one fewer turning point than the degree of the polynomial or one fewer than the number of factors.
A
continuous function has no breaks in its graph: the graph can be drawn without lifting the pen from the paper. A
smooth curve is a graph that has no sharp corners. The turning points of a smooth graph must always occur at rounded curves. The graphs of polynomial functions are both continuous and smooth.
Intercepts and turning points of polynomials
A polynomial of degree
$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ will have, at most,
$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$x -intercepts and
$\text{\hspace{0.17em}}n-1\text{\hspace{0.17em}}$ turning points.
Determining the number of intercepts and turning points of a polynomial
Without graphing the function, determine the local behavior of the function by finding the maximum number of
x -intercepts and turning points for
$\text{\hspace{0.17em}}f(x)=-3{x}^{10}+4{x}^{7}-{x}^{4}+2{x}^{3}.$
The polynomial has a degree of
$\text{\hspace{0.17em}}10,\text{\hspace{0.17em}}$ so there are at most 10
x -intercepts and at most 9 turning points.
Without graphing the function, determine the maximum number of
x -intercepts and turning points for
$\text{\hspace{0.17em}}f(x)=108-13{x}^{9}-8{x}^{4}+14{x}^{12}+2{x}^{3}.$
There are at most 12
$\text{\hspace{0.17em}}x\text{-}$ intercepts and at most 11 turning points.
Drawing conclusions about a polynomial function from the graph
What can we conclude about the polynomial represented by the graph shown in
[link] based on its intercepts and turning points?
The end behavior of the graph tells us this is the graph of an even-degree polynomial. See
[link] .
The graph has 2
x -intercepts, suggesting a degree of 2 or greater, and 3 turning points, suggesting a degree of 4 or greater. Based on this, it would be reasonable to conclude that the degree is even and at least 4.
What can we conclude about the polynomial represented by the graph shown in
[link] based on its intercepts and turning points?
The end behavior indicates an odd-degree polynomial function; there are 3
$\text{\hspace{0.17em}}x\text{-}$ intercepts and 2 turning points, so the degree is odd and at least 3. Because of the end behavior, we know that the lead coefficient must be negative.
Given the function
$\text{\hspace{0.17em}}f(x)=0.2(x-2)(x+1)(x-5),\text{\hspace{0.17em}}$ determine the local behavior.
The
$\text{\hspace{0.17em}}x\text{-}$ intercepts are
$\text{\hspace{0.17em}}(2,0),(-1,0),$ and
$\text{\hspace{0.17em}}(5,0),\text{\hspace{0.17em}}$ the
y- intercept is
$\text{\hspace{0.17em}}(0,\text{2}),\text{\hspace{0.17em}}$ and the graph has at most 2 turning points.
The anwser is imaginary
number if you want to know The anwser of the expression
you must arrange The expression and use quadratic formula To find the
answer
master
The anwser is imaginary
number if you want to know The anwser of the expression
you must arrange The expression and use quadratic formula To find the
answer
master
Y
master
X2-2X+8-4X2+12X-20=0
(X2-4X2)+(-2X+12X)+(-20+8)= 0
-3X2+10X-12=0
3X2-10X+12=0
Use quadratic formula To find the answer
answer (5±Root11i)/3
master
Soo sorry (5±Root11* i)/3
master
x2-2x+8-4x2+12x-20
x2-4x2-2x+12x+8-20
-3x2+10x-12
now you can find the answer using quadratic
Mukhtar
explain and give four example of hyperbolic function
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
the Cayley hamilton Theorem state if A is a square matrix and if f(x) is its characterics polynomial then f(x)=0 in another ways evey square matrix is a root of its chatacteristics polynomial.