 7.2.1: The formula for the distance d from to is _____.
 7.2.2: To complete the square of add .
 7.2.3: Use the Square Root Method to find the real solutions of 1x + 42
 7.2.4: The point that is symmetric with respect to the xaxis to the point...
 7.2.5: To graph shift the graph of to the right units and then 1 unit.
 7.2.6: A(n) is the collection of all points in the plane such that the dis...
 7.2.7: If the equation of the parabola is of the form (a) (b) (c) (d)
 7.2.8: The coordinates of the vertex are .
 7.2.9: If then the coordinates of the focus are .
 7.2.10: If then the equation of the directrix is .
 7.2.11: In 1118, the graph of a parabola is given. Match each graph to its ...
 7.2.12: In 1118, the graph of a parabola is given. Match each graph to its ...
 7.2.13: In 1118, the graph of a parabola is given. Match each graph to its ...
 7.2.14: In 1118, the graph of a parabola is given. Match each graph to its ...
 7.2.15: In 1118, the graph of a parabola is given. Match each graph to its ...
 7.2.16: In 1118, the graph of a parabola is given. Match each graph to its ...
 7.2.17: In 1118, the graph of a parabola is given. Match each graph to its ...
 7.2.18: In 1118, the graph of a parabola is given. Match each graph to its ...
 7.2.19: Focus at vertex at 14, 02; 10, 02
 7.2.20: Focus at vertex at 10, 22; 10, 02
 7.2.21: Focus at vertex at 10, 32; 10, 02 2
 7.2.22: Focus at vertex at 14, 02; 10, 02
 7.2.23: Focus at directrix the line 12, 02; x = 2
 7.2.24: Focus at directrix the line 10, 12; y = 1
 7.2.25: Directrix the line vertex at y =  10, 02
 7.2.26: Directrix the line vertex at x =  10, 02
 7.2.27: Vertex at axis of symmetry the yaxis; containing the point 12, 32
 7.2.28: Vertex at axis of symmetry the xaxis; containing the point 12, 32
 7.2.29: Vertex at focus at 12, 32; 12, 52
 7.2.30: Vertex at focus at 14, 22; 16, 22
 7.2.31: Vertex at focus at 11, 22; 10, 22 3
 7.2.32: Vertex at focus at 13, 02; 13, 22
 7.2.33: Focus at directrix the line 13, 42; y = 2
 7.2.34: Focus at directrix the line 12, 42; x = 4
 7.2.35: Focus at directrix the line 13, 22; x = 1 3
 7.2.36: Focus at directrix the line 14, 42; y = 2
 7.2.37: x2 = 4y
 7.2.38: y2 = 8x
 7.2.39: y2 = 16x
 7.2.40: x2 = 4y
 7.2.41: 1y  222 = 81x + 12 4
 7.2.42: 1x + 422 = 161y + 22
 7.2.43: 1x  322 = 1y + 12 4
 7.2.44: 1y + 122 = 41x  22
 7.2.45: 1y + 322 = 81x  22 4
 7.2.46: 1x  222 = 41y  32
 7.2.47: y2  4y + 4x + 4 = 0
 7.2.48: x2 + 6x  4y + 1 = 0
 7.2.49: x2 + 8x = 4y  8
 7.2.50: y2  2y = 8x  1
 7.2.51: y2 + 2y  x = 0
 7.2.52: x2  4x = 2y
 7.2.53: x2  4x = y + 4
 7.2.54: In 5562, write an equation for each parabola.
 7.2.55: In 5562, write an equation for each parabola.
 7.2.56: In 5562, write an equation for each parabola.
 7.2.57: In 5562, write an equation for each parabola.
 7.2.58: In 5562, write an equation for each parabola.
 7.2.59: In 5562, write an equation for each parabola.
 7.2.60: In 5562, write an equation for each parabola.
 7.2.61: In 5562, write an equation for each parabola.
 7.2.62: In 5562, write an equation for each parabola.
 7.2.63: Satellite Dish A satellite dish is shaped like a paraboloid of revo...
 7.2.64: Constructing a TV Dish A cable TV receiving dish is in the shape of...
 7.2.65: Constructing a TV Dish A cable TV receiving dish is in the shape of...
 7.2.66: Constructing a Headlight A sealedbeam headlight is in the shape of...
 7.2.67: Suspension Bridge The cables of a suspension bridge are in the shap...
 7.2.68: Suspension Bridge The cables of a suspension bridge are in the shap...
 7.2.69: Searchlight A searchlight is shaped like a paraboloid of revolution...
 7.2.70: Searchlight A searchlight is shaped like a paraboloid of revolution...
 7.2.71: Solar Heat A mirror is shaped like a paraboloid of revolution and w...
 7.2.72: Reflecting Telescope A reflecting telescope contains a mirror shape...
 7.2.73: Parabolic Arch Bridge A bridge is built in the shape of a parabolic...
 7.2.74: Parabolic Arch Bridge A bridge is to be built in the shape of a par...
 7.2.75: Gateway Arch The Gateway Arch in St. Louis is often mistaken to be ...
 7.2.76: Show that an equation of the form is the equation of a parabola wit...
 7.2.77: Show that an equation of the form is the equation of a parabola wit...
 7.2.78: Show that the graph of an equation of the form (a) Is a parabola if...
 7.2.79: Show that the graph of an equation of the form (a) Is a parabola if...
Solutions for Chapter 7.2: The Parabola
Full solutions for College Algebra  9th Edition
ISBN: 9780321716811
Solutions for Chapter 7.2: The Parabola
Get Full SolutionsCollege Algebra was written by and is associated to the ISBN: 9780321716811. Since 79 problems in chapter 7.2: The Parabola have been answered, more than 30722 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 7.2: The Parabola includes 79 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra, edition: 9.

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).

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

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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.

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.

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.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

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).

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

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

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

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

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

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