 9.3.1: Is each algebraic expression a polynomial? If so, how many terms do...
 9.3.2: Expand each expression. On your calculator, enter the original expr...
 9.3.3: Copy each rectangle diagram and fill in the missing values. Then wr...
 9.3.4: Convert each equation from vertex form to general form. Check your ...
 9.3.5: Draw a rectangle diagram to represent each expression. Then write a...
 9.3.6: Consider the graph of the parabola y = x2 4x + 7.a. What are the co...
 9.3.7: Heather thinks she has found a shortcut to the rectangle diagram me...
 9.3.8: APPLICATION The quadratic equation y = 0.0056x2 + 0.14x relates a v...
 9.3.9: The function h(t) = 4.9(t 0.4)2 + 2.5 describes the height of a sof...
 9.3.10: Is the expression on the right equivalent to the expression on the ...
 9.3.11: APPLICATION The Yoyo Warehouse uses the equation y = 85x2 + 552.5x...
 9.3.12: Use a threebythree rectangle diagram to square each trinomial. a....
 9.3.13: What is the general form of y = (x + 4)2? Write a paragraph describ...
 9.3.14: Is this parabola a graph of a function?
 9.3.15: Use the graph of f (x) to evaluate each expression. Then think of t...
 9.3.16: The equation y = 0.0024x2 + 0.81x + 2.0 models the path of a golf b...
Solutions for Chapter 9.3: From Vertex to General Form
Full solutions for Discovering Algebra: An Investigative Approach  2nd Edition
ISBN: 9781559537636
Solutions for Chapter 9.3: From Vertex to General Form
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Discovering Algebra: An Investigative Approach, edition: 2. Since 16 problems in chapter 9.3: From Vertex to General Form have been answered, more than 2889 students have viewed full stepbystep solutions from this chapter. Chapter 9.3: From Vertex to General Form includes 16 full stepbystep solutions. Discovering Algebra: An Investigative Approach was written by Patricia and is associated to the ISBN: 9781559537636.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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].

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.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

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

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

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.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

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.

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

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

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.
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