 10.4.1: A/an ______________ is the set of points in a plane that are equidi...
 10.4.2: The graph of x = a(y  k) 2 + h or x = ay2 + by + c opens to the ri...
 10.4.3: The graph of x = a(y  k) 2 + h or x = ay2 + by + c opens to the le...
 10.4.4: Determine whether the graph of each equation opens upward, downward...
 10.4.5: Determine whether the graph of each equation opens upward, downward...
 10.4.6: Determine whether the graph of each equation opens upward, downward...
 10.4.7: Determine whether the graph of each equation opens upward, downward...
 10.4.8: Determine whether the graph of each equation opens upward, downward...
 10.4.9: Determine whether the graph of each equation opens upward, downward...
 10.4.10: Determine whether the graph of each equation opens upward, downward...
 10.4.11: Determine whether the graph of each equation opens upward, downward...
 10.4.12: Determine whether the graph of each equation opens upward, downward...
 10.4.13: The vertex of x = a(y  k) 2 + h is ______________ .
 10.4.14: The ycoordinate of the vertex of x = ay2 + by + c is y = _________...
 10.4.15: The circle, ellipse, hyperbola, and parabola are examples of ______...
 10.4.16: In Exercises 718, find the coordinates of the vertex for the horizo...
 10.4.17: In Exercises 718, find the coordinates of the vertex for the horizo...
 10.4.18: In Exercises 718, find the coordinates of the vertex for the horizo...
 10.4.19: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.20: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.21: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.22: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.23: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.24: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.25: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.26: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.27: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.28: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.29: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.30: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.31: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.32: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.33: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.34: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.35: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.36: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.37: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.38: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.39: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.40: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.41: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.42: In Exercises 1942, use the vertex and intercepts to sketch the grap...
 10.4.43: In Exercises 4354, the equation of a parabola is given. Determine: ...
 10.4.44: In Exercises 4354, the equation of a parabola is given. Determine: ...
 10.4.45: In Exercises 4354, the equation of a parabola is given. Determine: ...
 10.4.46: In Exercises 4354, the equation of a parabola is given. Determine: ...
 10.4.47: In Exercises 4354, the equation of a parabola is given. Determine: ...
 10.4.48: In Exercises 4354, the equation of a parabola is given. Determine: ...
 10.4.49: In Exercises 4354, the equation of a parabola is given. Determine: ...
 10.4.50: In Exercises 4354, the equation of a parabola is given. Determine: ...
 10.4.51: In Exercises 4354, the equation of a parabola is given. Determine: ...
 10.4.52: In Exercises 4354, the equation of a parabola is given. Determine: ...
 10.4.53: In Exercises 4354, the equation of a parabola is given. Determine: ...
 10.4.54: In Exercises 4354, the equation of a parabola is given. Determine: ...
 10.4.55: In Exercises 5564, indicate whether the graph of each equation is a...
 10.4.56: In Exercises 5564, indicate whether the graph of each equation is a...
 10.4.57: In Exercises 5564, indicate whether the graph of each equation is a...
 10.4.58: In Exercises 5564, indicate whether the graph of each equation is a...
 10.4.59: In Exercises 5564, indicate whether the graph of each equation is a...
 10.4.60: In Exercises 5564, indicate whether the graph of each equation is a...
 10.4.61: In Exercises 5564, indicate whether the graph of each equation is a...
 10.4.62: In Exercises 5564, indicate whether the graph of each equation is a...
 10.4.63: In Exercises 5564, indicate whether the graph of each equation is a...
 10.4.64: In Exercises 5564, indicate whether the graph of each equation is a...
 10.4.65: In Exercises 6574, indicate whether the graph of each equation is a...
 10.4.66: In Exercises 6574, indicate whether the graph of each equation is a...
 10.4.67: In Exercises 6574, indicate whether the graph of each equation is a...
 10.4.68: In Exercises 6574, indicate whether the graph of each equation is a...
 10.4.69: In Exercises 6574, indicate whether the graph of each equation is a...
 10.4.70: In Exercises 6574, indicate whether the graph of each equation is a...
 10.4.71: In Exercises 6574, indicate whether the graph of each equation is a...
 10.4.72: In Exercises 6574, indicate whether the graph of each equation is a...
 10.4.73: In Exercises 6574, indicate whether the graph of each equation is a...
 10.4.74: In Exercises 6574, indicate whether the graph of each equation is a...
 10.4.75: In Exercises 7580, use the vertex and the direction in which the pa...
 10.4.76: In Exercises 7580, use the vertex and the direction in which the pa...
 10.4.77: In Exercises 7580, use the vertex and the direction in which the pa...
 10.4.78: In Exercises 7580, use the vertex and the direction in which the pa...
 10.4.79: In Exercises 7580, use the vertex and the direction in which the pa...
 10.4.80: In Exercises 7580, use the vertex and the direction in which the pa...
 10.4.81: In Exercises 8186, find the solution set for each system by graphin...
 10.4.82: In Exercises 8186, find the solution set for each system by graphin...
 10.4.83: In Exercises 8186, find the solution set for each system by graphin...
 10.4.84: In Exercises 8186, find the solution set for each system by graphin...
 10.4.85: In Exercises 8186, find the solution set for each system by graphin...
 10.4.86: In Exercises 8186, find the solution set for each system by graphin...
 10.4.87: The George Washington Bridge spans the Hudson River from New York t...
 10.4.88: The towers of the Golden Gate Bridge connecting San Francisco to Ma...
 10.4.89: A satellite dish is in the shape of a parabolic surface. Signals co...
 10.4.90: An engineer is designing a flashlight using a parabolic reflecting ...
 10.4.91: Moir patterns, such as those shown in Exercises 9192, can appear wh...
 10.4.92: Moir patterns, such as those shown in Exercises 9192, can appear wh...
 10.4.93: What is a parabola?
 10.4.94: If you are given an equation of a parabola, explain how to determin...
 10.4.95: Explain how to use x = 2(y + 3) 2  5 to find the parabolas vertex.
 10.4.96: Explain how to use x = y2 + 8y + 9 to find the parabolas vertex.
 10.4.97: Describe one similarity and one difference between the graphs of x ...
 10.4.98: How can you distinguish parabolas from other conic sections by look...
 10.4.99: How can you distinguish ellipses from hyperbolas by looking at thei...
 10.4.100: How can you distinguish ellipses from circles by looking at their e...
 10.4.101: Use a graphing utility to graph the parabolas in Exercises 101102. ...
 10.4.102: Use a graphing utility to graph the parabolas in Exercises 101102. ...
 10.4.103: Use a graphing utility to graph any three of the parabolas that you...
 10.4.104: Make Sense? In Exercises 104107, determine whether each statement m...
 10.4.105: Make Sense? In Exercises 104107, determine whether each statement m...
 10.4.106: Make Sense? In Exercises 104107, determine whether each statement m...
 10.4.107: Make Sense? In Exercises 104107, determine whether each statement m...
 10.4.108: In Exercises 108111, determine whether each statement is true or fa...
 10.4.109: In Exercises 108111, determine whether each statement is true or fa...
 10.4.110: In Exercises 108111, determine whether each statement is true or fa...
 10.4.111: In Exercises 108111, determine whether each statement is true or fa...
 10.4.112: Look at the satellite dish shown in Exercise 89. Why must the recei...
 10.4.113: The parabolic arch shown in the figure is 50 feet above the water a...
 10.4.114: Graph: f(x) = 21x . (Section 9.1, Example 4)
 10.4.115: If f(x) = 1 3 x  5, find f 1 (x). (Section 9.2, Example 4)
 10.4.116: Solve: (x + 1) 2 + (x + 3) 2 = 4. (Section 5.7, Example 2)
 10.4.117: Exercises 117119 will help you prepare for the material covered in ...
 10.4.118: Exercises 117119 will help you prepare for the material covered in ...
 10.4.119: Exercises 117119 will help you prepare for the material covered in ...
Solutions for Chapter 10.4: The Parabola; Identifying Conic Sections
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 10.4: The Parabola; Identifying Conic Sections
Get Full SolutionsChapter 10.4: The Parabola; Identifying Conic Sections includes 119 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 119 problems in chapter 10.4: The Parabola; Identifying Conic Sections have been answered, more than 52996 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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

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

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

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.

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.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.