 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 9077 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.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Column space C (A) =
space of all combinations of the columns of A.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

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.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

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

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

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

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

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

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

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

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