 73.1: y = x + 2 2
 73.2: y = 4x 3
 73.3: y = x  1 + 3 FI
 73.4: Determine an equation that will give the maximum height of the wate...
 73.5: The Coolville Fire Department must purchase a pump that will propel...
 73.6: y x  4 + 1 7.
 73.7: y > 2x + 4 8.
 73.8: y x + 2  1 Gra
 73.9: y = 3x 10
 73.10: y =  5x 11
 73.11: y = 4 x
 73.12: y = _1 2 x 13
 73.13: y = x + 2 14.
 73.14: y = x  7 15
 73.15: y =  2x + 1 16.
 73.16: y = 5x  3
 73.17: y = x + 6  3
 73.18: y = 5  x + 4
 73.19: y = 3x  6 + 4
 73.20: y = 2 3  4x + 3
 73.21: ROLLER COASTERS The velocity of a roller coaster as it moves down a...
 73.22: An astronaut weighs 140 pounds on Earth and 120 pounds in space. Ho...
 73.23: An astronaut weighs 125 pounds on Earth. What is her weight in spac...
 73.24: y 6 x
 73.25: y < x + 5 26.
 73.26: y > 2x + 8 27
 73.27: y 5x  8 28.
 73.28: y x  3 + 4 29.
 73.29: y < 6x  2 + 1 Ex
 73.30: OPEN ENDED Write a square root function with a domain of {x  x 2}.
 73.31: CHALLENGE Recall how values of a, h, and k can affect the graph of ...
 73.32: REASONING Describe the difference between the graphs of y = x  4 a...
 73.33: Writing in Math Refer to the information on page 397 to explain how...
 73.34: ACT/SAT Given the graph of the square root function at the right, w...
 73.35: REVIEW For a game, Patricia must roll a die and draw a card from a ...
 73.36: f (x) = 3x g(x) = _1 3 x g
 73.37: f (x) = 4x  5 3 g(x) =_14x _516 g
 73.38: f (x) = _3x + 2 7 g(x) =_7x  23
 73.39: f (x) = x + 5 4 g(x) = x  3
 73.40: f (x) = 10x  20 4 g(x) = x  2 g
 73.41: f (x) = 4 x 2  9 g(x) = _12x + 3
 73.42: BIOLOGY Humans blink their eyes about once every 5 seconds. How man...
 73.43: 4.63 4
 73.45: 16 3
 73.46: 8.333
 73.47: 7.323223222
Solutions for Chapter 73: Square Root Functions and Inequalities
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 73: Square Root Functions and Inequalities
Get Full SolutionsThis textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. Chapter 73: Square Root Functions and Inequalities includes 46 full stepbystep solutions. Since 46 problems in chapter 73: Square Root Functions and Inequalities have been answered, more than 52871 students have viewed full stepbystep solutions from this chapter. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. This expansive textbook survival guide covers the following chapters and their solutions.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

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

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

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].

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

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

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

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

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

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

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