 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 47357 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.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

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

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

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

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)ยท(b  Ax) = o.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.