 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 9584 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.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

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

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.

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!).

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

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

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).

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

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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 ().

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).
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