 3.1: In Exercises 1 and 2, graph each function. Compare the graph of eac...
 3.2: In Exercises 1 and 2, graph each function. Compare the graph of eac...
 3.3: In Exercises 314, write the quadratic function in standard form and...
 3.4: In Exercises 314, write the quadratic function in standard form and...
 3.5: In Exercises 314, write the quadratic function in standard form and...
 3.6: In Exercises 314, write the quadratic function in standard form and...
 3.7: In Exercises 314, write the quadratic function in standard form and...
 3.8: In Exercises 314, write the quadratic function in standard form and...
 3.9: In Exercises 314, write the quadratic function in standard form and...
 3.10: In Exercises 314, write the quadratic function in standard form and...
 3.11: In Exercises 314, write the quadratic function in standard form and...
 3.12: In Exercises 314, write the quadratic function in standard form and...
 3.13: In Exercises 314, write the quadratic function in standard form and...
 3.14: In Exercises 314, write the quadratic function in standard form and...
 3.15: In Exercises 1520, write the standard form of the equation of the p...
 3.16: In Exercises 1520, write the standard form of the equation of the p...
 3.17: In Exercises 1520, write the standard form of the equation of the p...
 3.18: In Exercises 1520, write the standard form of the equation of the p...
 3.19: In Exercises 1520, write the standard form of the equation of the p...
 3.20: In Exercises 1520, write the standard form of the equation of the p...
 3.21: NUMERICAL, GRAPHICAL, AND ANALYTICAL ANALYSIS A rectangle is inscri...
 3.22: GEOMETRY The perimeter of a rectangle is 200 meters. (a) Draw a dia...
 3.23: MAXIMUM REVENUE The total revenue earned (in dollars) from producin...
 3.24: MAXIMUM PROFIT A real estate office handles an apartment building t...
 3.25: MINIMUM COST A softdrink manufacturer has daily production costs o...
 3.26: SOCIOLOGY The average age of the groom at a first marriage for a gi...
 3.27: In Exercises 2732, sketch the graphs of and the transformation.
 3.28: In Exercises 2732, sketch the graphs of and the transformation.
 3.29: In Exercises 2732, sketch the graphs of and the transformation.
 3.30: In Exercises 2732, sketch the graphs of and the transformation.
 3.31: In Exercises 2732, sketch the graphs of and the transformation.
 3.32: In Exercises 2732, sketch the graphs of and the transformation.
 3.33: In Exercises 3336, describe the righthand and lefthand behavior o...
 3.34: In Exercises 3336, describe the righthand and lefthand behavior o...
 3.35: In Exercises 3336, describe the righthand and lefthand behavior o...
 3.36: In Exercises 3336, describe the righthand and lefthand behavior o...
 3.37: In Exercises 37 42, find all the real zeros of the polynomial funct...
 3.38: In Exercises 37 42, find all the real zeros of the polynomial funct...
 3.39: In Exercises 37 42, find all the real zeros of the polynomial funct...
 3.40: In Exercises 37 42, find all the real zeros of the polynomial funct...
 3.41: In Exercises 37 42, find all the real zeros of the polynomial funct...
 3.42: In Exercises 37 42, find all the real zeros of the polynomial funct...
 3.43: In Exercises 43 46, sketch the graph of the function by (a) applyin...
 3.44: In Exercises 43 46, sketch the graph of the function by (a) applyin...
 3.45: In Exercises 43 46, sketch the graph of the function by (a) applyin...
 3.46: In Exercises 43 46, sketch the graph of the function by (a) applyin...
 3.47: In Exercises 4750, (a) use the Intermediate Value Theorem and the t...
 3.48: In Exercises 4750, (a) use the Intermediate Value Theorem and the t...
 3.49: In Exercises 4750, (a) use the Intermediate Value Theorem and the t...
 3.50: In Exercises 4750, (a) use the Intermediate Value Theorem and the t...
 3.51: In Exercises 5156, use long division to divide.
 3.52: In Exercises 5156, use long division to divide.
 3.53: In Exercises 5156, use long division to divide.
 3.54: In Exercises 5156, use long division to divide.
 3.55: In Exercises 5156, use long division to divide.
 3.56: In Exercises 5156, use long division to divide.
 3.57: In Exercises 57 60, use synthetic division to divide.
 3.58: In Exercises 57 60, use synthetic division to divide.
 3.59: In Exercises 57 60, use synthetic division to divide.
 3.60: In Exercises 57 60, use synthetic division to divide.
 3.61: In Exercises 61 and 62, use synthetic division to determine whether...
 3.62: In Exercises 61 and 62, use synthetic division to determine whether...
 3.63: In Exercises 63 and 64, use the Remainder Theorem and synthetic div...
 3.64: In Exercises 63 and 64, use the Remainder Theorem and synthetic div...
 3.65: In Exercises 65 68, (a) verify the given factor(s) of the function ...
 3.66: In Exercises 65 68, (a) verify the given factor(s) of the function ...
 3.67: In Exercises 65 68, (a) verify the given factor(s) of the function ...
 3.68: In Exercises 65 68, (a) verify the given factor(s) of the function ...
 3.69: In Exercises 6974, find all the zeros of the function.
 3.70: In Exercises 6974, find all the zeros of the function.
 3.71: In Exercises 6974, find all the zeros of the function.
 3.72: In Exercises 6974, find all the zeros of the function.
 3.73: In Exercises 6974, find all the zeros of the function.
 3.74: In Exercises 6974, find all the zeros of the function.
 3.75: In Exercises 75 and 76, use the Rational Zero Test to list all poss...
 3.76: In Exercises 75 and 76, use the Rational Zero Test to list all poss...
 3.77: In Exercises 7782, find all the rational zeros of the function.
 3.78: In Exercises 7782, find all the rational zeros of the function.
 3.79: In Exercises 7782, find all the rational zeros of the function.
 3.80: In Exercises 7782, find all the rational zeros of the function.
 3.81: In Exercises 7782, find all the rational zeros of the function.
 3.82: In Exercises 7782, find all the rational zeros of the function.
 3.83: In Exercises 83 and 84, find a polynomial function with real coeffi...
 3.84: In Exercises 83 and 84, find a polynomial function with real coeffi...
 3.85: In Exercises 8588, use the given zero to find all the zeros of the ...
 3.86: In Exercises 8588, use the given zero to find all the zeros of the ...
 3.87: In Exercises 8588, use the given zero to find all the zeros of the ...
 3.88: In Exercises 8588, use the given zero to find all the zeros of the ...
 3.89: In Exercises 8992, find all the zeros of the function and write the...
 3.90: In Exercises 8992, find all the zeros of the function and write the...
 3.91: In Exercises 8992, find all the zeros of the function and write the...
 3.92: In Exercises 8992, find all the zeros of the function and write the...
 3.93: In Exercises 9396, use a graphing utility to (a) graph the function...
 3.94: In Exercises 9396, use a graphing utility to (a) graph the function...
 3.95: In Exercises 9396, use a graphing utility to (a) graph the function...
 3.96: In Exercises 9396, use a graphing utility to (a) graph the function...
 3.97: In Exercises 97 and 98, use Descartess Rule of Signs to determine t...
 3.98: In Exercises 97 and 98, use Descartess Rule of Signs to determine t...
 3.99: In Exercises 99 and 100, use synthetic division to verify the upper...
 3.100: In Exercises 99 and 100, use synthetic division to verify the upper...
 3.101: COMPACT DISCS The values (in billions of dollars) of shipments of c...
 3.102: DATA ANALYSIS: TV USAGE The table shows the projected numbers of ho...
 3.103: MEASUREMENT You notice a billboard indicating that it is 2.5 miles ...
 3.104: ENERGY The power produced by a wind turbine is proportional to the ...
 3.105: FRICTIONAL FORCE The frictional force between the tires and the roa...
 3.106: DEMAND A company has found that the daily demand for its boxes of c...
 3.107: TRAVEL TIME The travel time between two cities is inversely proport...
 3.108: COST The cost of constructing a wooden box with a square base varie...
 3.109: A fourthdegree polynomial with real coefficients can have and 5 as...
 3.110: If is directly proportional to then is directly proportional to
 3.111: WRITING Explain how to determine the maximum or minimum value of a ...
 3.112: WRITING Explain the connections between factors of a polynomial, ze...
Solutions for Chapter 3: Polynomial Functions
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter 3: Polynomial Functions
Get Full SolutionsChapter 3: Polynomial Functions includes 112 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9781439048696. Since 112 problems in chapter 3: Polynomial Functions have been answered, more than 33402 students have viewed full stepbystep solutions from this chapter.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Iterative method.
A sequence of steps intended to approach the desired solution.

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

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

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

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.