 6.4.1: State the degree and leading coefficient of each polynomial in one ...
 6.4.2: State the degree and leading coefficient of each polynomial in one ...
 6.4.3: Find p(3) and p(1) for each function
 6.4.4: Find p(3) and p(1) for each function
 6.4.5: The intensity of light emitted by a firefly can be determined by L(...
 6.4.6: If p(x) = 2x3 + 6x  12 and q(x) = 5x2 + 4, find each value
 6.4.7: If p(x) = 2x3 + 6x  12 and q(x) = 5x2 + 4, find each value
 6.4.8: If p(x) = 2x3 + 6x  12 and q(x) = 5x2 + 4, find each value
 6.4.9: For each graph, a. describe the end behavior, b. determine whether ...
 6.4.10: For each graph, a. describe the end behavior, b. determine whether ...
 6.4.11: For each graph, a. describe the end behavior, b. determine whether ...
 6.4.12: State the degree and leading coefficient of each polynomial in one ...
 6.4.13: State the degree and leading coefficient of each polynomial in one ...
 6.4.14: State the degree and leading coefficient of each polynomial in one ...
 6.4.15: State the degree and leading coefficient of each polynomial in one ...
 6.4.16: State the degree and leading coefficient of each polynomial in one ...
 6.4.17: State the degree and leading coefficient of each polynomial in one ...
 6.4.18: Find p(4) and p(2) for each function.
 6.4.19: Find p(4) and p(2) for each function.
 6.4.20: Find p(4) and p(2) for each function.
 6.4.21: Find p(4) and p(2) for each function.
 6.4.22: If p(x) = 3x2  2x + 5 and r(x) = x3 + x + 1, find each value.
 6.4.23: If p(x) = 3x2  2x + 5 and r(x) = x3 + x + 1, find each value.
 6.4.24: If p(x) = 3x2  2x + 5 and r(x) = x3 + x + 1, find each value.
 6.4.25: If p(x) = 3x2  2x + 5 and r(x) = x3 + x + 1, find each value.
 6.4.26: If p(x) = 3x2  2x + 5 and r(x) = x3 + x + 1, find each value.
 6.4.27: If p(x) = 3x2  2x + 5 and r(x) = x3 + x + 1, find each value.
 6.4.28: For each graph, a. describe the end behavior, b. determine whether ...
 6.4.29: For each graph, a. describe the end behavior, b. determine whether ...
 6.4.30: For each graph, a. describe the end behavior, b. determine whether ...
 6.4.31: For each graph, a. describe the end behavior, b. determine whether ...
 6.4.32: For each graph, a. describe the end behavior, b. determine whether ...
 6.4.33: For each graph, a. describe the end behavior, b. determine whether ...
 6.4.34: The power generated by a windmill is a function of the speed of the...
 6.4.35: For a moving object with mass m in kilograms, the kinetic energy KE...
 6.4.36: Find p(4) and p(2) for each function.
 6.4.37: Find p(4) and p(2) for each function.
 6.4.38: Find p(4) and p(2) for each function.
 6.4.39: Find p(4) and p(2) for each function.
 6.4.40: If p(x) = 3x2  2x + 5 and r(x) = x3 + x + 1, find each value.
 6.4.41: If p(x) = 3x2  2x + 5 and r(x) = x3 + x + 1, find each value.
 6.4.42: If p(x) = 3x2  2x + 5 and r(x) = x3 + x + 1, find each value.
 6.4.43: Is the graph an odddegree or evendegree function?
 6.4.44: Discuss the end behavior
 6.4.45: Do you think attendance at Broadway plays will increase or decrease...
 6.4.46: The number of regions formed by connecting n points of a circle can...
 6.4.47: Find the number of regions formed by connecting 5 points of a circl...
 6.4.48: How many points would you have to connect to form 99 regions?
 6.4.49: Explain why a constant polynomial such as f(x) = 4 has degree 0 and...
 6.4.50: Sketch the graph of an odddegree polynomial function with a negati...
 6.4.51: Determine whether the following statement is always, sometimes or n...
 6.4.52: For Exercises 5255, use the following information. The graph of the...
 6.4.53: For Exercises 5255, use the following information. The graph of the...
 6.4.54: For Exercises 5255, use the following information. The graph of the...
 6.4.55: For Exercises 5255, use the following information. The graph of the...
 6.4.56: Use the information on page 331 to explain where polynomial functio...
 6.4.57: The figure at the right shows the graph of a polynomial function f(...
 6.4.58: Which polynomial represents (4x2 + 5x  3)(2x  7)? F 8x3  18x2  ...
 6.4.59: Simplify.
 6.4.60: Simplify.
 6.4.61: Simplify.
 6.4.62: Simplify.
 6.4.63: Ms. Schifflet is writing a computer program to find the salaries of...
 6.4.64: Solve each equation by completing the square.
 6.4.65: Solve each equation by completing the square.
 6.4.66: Write an absolute value inequality for each graph
 6.4.67: Write an absolute value inequality for each graph
 6.4.68: Write an absolute value inequality for each graph
 6.4.69: Write an absolute value inequality for each graph
 6.4.70: Name the property illustrated by each statement
 6.4.71: Name the property illustrated by each statement
 6.4.72: Name the property illustrated by each statement
 6.4.73: Graph each equation by making a table of values
 6.4.74: Graph each equation by making a table of values
 6.4.75: Graph each equation by making a table of values
Solutions for Chapter 6.4: Polynomial Functions
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 6.4: Polynomial Functions
Get Full SolutionsSince 75 problems in chapter 6.4: Polynomial Functions have been answered, more than 96645 students have viewed full stepbystep solutions from this chapter. Chapter 6.4: Polynomial Functions includes 75 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. California Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568. This textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Outer product uv T
= column times row = rank one matrix.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.