 Chapter 5.1: f(1)
 Chapter 5.2: f(4)
 Chapter 5.3: f(0)
 Chapter 5.4: f(2)
 Chapter 5.5: g(0)
 Chapter 5.6: g(1)
 Chapter 5.7: g(2)
 Chapter 5.8: g(0.5)
 Chapter 5.9: Write a function that is a model for the situation.
 Chapter 5.10: Evaluate the function to estimate how far a 2yearold tuna has tra...
 Chapter 5.11: x 2 + 11x + 30
 Chapter 5.12: x 2 13x + 36
 Chapter 5.13: x 2 x 56
 Chapter 5.14: x 2 5x 14
 Chapter 5.15: x 2 + x + 2
 Chapter 5.16: x 2 + 10x + 25
 Chapter 5.17: x 2 22x + 121
 Chapter 5.18: x 2 9
 Chapter 5.19: FLOOR PLAN A living room has a floor space of x 2 + 11x + 28 square...
 Chapter 5.20: i 89
 Chapter 5.21: (6  4i)(6 + 4i) 2
 Chapter 5.22: 2  4i 1 + 3i
 Chapter 5.23: ELECTRICITY The impedance in one part of a series circuit is 2 + 5j...
 Chapter 5.24: 3 x 2 + 6x + 3 = 0
 Chapter 5.25: 5 y 2 = 80
 Chapter 5.26: 25 x 2  30x = 9
 Chapter 5.27: 6 x 2 + 7x = 3
 Chapter 5.28: 2 c 2 + 18c  44 = 0
 Chapter 5.29: TRIANGLES Find the dimensions of a triangle if the base is _2 3 the...
 Chapter 5.30: 45
 Chapter 5.31: 64 n 3 3
 Chapter 5.32: 64 m 12 33
 Chapter 5.33: (7  4i)  (3 + 6i)
 Chapter 5.34: (3 + 4i)(5  2i)
 Chapter 5.35: ( 6 + i)( 6  i) 3
 Chapter 5.36: _1 + i 1  i 3
 Chapter 5.37: 4  3i 1 + 2i
 Chapter 5.38: ELECTRICITY The impedance in one part of a series circuit is 2 + 3j...
 Chapter 5.39: x 2 + 34x + c
 Chapter 5.40: x 2  11x + c
 Chapter 5.41: 2 x 2  7x  15 = 0
 Chapter 5.42: 2 x 2  5x + 7 = 3
 Chapter 5.43: GARDENING Antoinette has a rectangular rose garden with the length ...
 Chapter 5.44: x 2 + 2x + 7 = 0
 Chapter 5.45: 2 x 2 + 12x  5 = 0
 Chapter 5.46: 3 x 2 + 7x  2 = 0
 Chapter 5.47: FOOTBALL The path of a football thrown across a field is given by t...
 Chapter 5.48: y = 6(x + 2 ) 2 + 3
 Chapter 5.49: y =  _1 3 x 2 + 8x
 Chapter 5.50: y = (x  2 ) 2  2
 Chapter 5.51: y = 2 x 2 + 8x + 10
 Chapter 5.52: NUMBER THEORY The graph shows the product of two numbers with a sum...
 Chapter 5.53: y > x 2  5x + 15
 Chapter 5.54: y  x 2 + 7x  11
 Chapter 5.55: 6 x 2 + 5x > 4
 Chapter 5.56: 8x + x 2 16
 Chapter 5.57: 4 x 2  9 4x
 Chapter 5.58: 3 x 2  5 > 6x
 Chapter 5.59: GAS MILEAGE The gas mileage y in miles per gallon for a particular ...
Solutions for Chapter Chapter 5: Quadratic Functions and Inequalities
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter Chapter 5: Quadratic Functions and Inequalities
Get Full SolutionsThis textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. Since 59 problems in chapter Chapter 5: Quadratic Functions and Inequalities have been answered, more than 60752 students have viewed full stepbystep solutions from this chapter. Chapter Chapter 5: Quadratic Functions and Inequalities includes 59 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Column space C (A) =
space of all combinations of the columns of A.

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

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

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

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.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

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)·(b  Ax) = o.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

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

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

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