 3.3.1: List the intercepts of the equation y = x2  9. (pp. 18 19)
 3.3.2: Find the real solutions of the equation 2x2 + 7x  4 = 0. (pp. A46 ...
 3.3.3: To complete the square of x2  5x, you add the number _______. (p. ...
 3.3.4: To graph y = (x  4)2 , you shift the graph of y = x2 to the ______...
 3.3.5: The graph of a quadratic function is called a(n) _________.
 3.3.6: The vertical line passing through the vertex of a parabola is calle...
 3.3.7: The xcoordinate of the vertex of f1x2 = ax2 + bx + c, a 0, is ____...
 3.3.8: The graph of f1x2 = 2x2 + 3x  4 opens up.
 3.3.9: The ycoordinate of the vertex of f1x2 = x2 + 4x + 5 is f 122.
 3.3.10: If the discriminant b2  4ac = 0, the graph of f1x2 = ax2 + bx + c,...
 3.3.11: In 1118, match each graph to one the following functions.
 3.3.12: In 1118, match each graph to one the following functions.
 3.3.13: In 1118, match each graph to one the following functions.
 3.3.14: In 1118, match each graph to one the following functions.
 3.3.15: In 1118, match each graph to one the following functions.
 3.3.16: In 1118, match each graph to one the following functions.
 3.3.17: In 1118, match each graph to one the following functions.
 3.3.18: In 1118, match each graph to one the following functions.
 3.3.19: In 1930, graph the function f by starting with the graph of y = x2 ...
 3.3.20: In 1930, graph the function f by starting with the graph of y = x2 ...
 3.3.21: In 1930, graph the function f by starting with the graph of y = x2 ...
 3.3.22: In 1930, graph the function f by starting with the graph of y = x2 ...
 3.3.23: In 1930, graph the function f by starting with the graph of y = x2 ...
 3.3.24: In 1930, graph the function f by starting with the graph of y = x2 ...
 3.3.25: In 1930, graph the function f by starting with the graph of y = x2 ...
 3.3.26: In 1930, graph the function f by starting with the graph of y = x2 ...
 3.3.27: In 1930, graph the function f by starting with the graph of y = x2 ...
 3.3.28: In 1930, graph the function f by starting with the graph of y = x2 ...
 3.3.29: In 1930, graph the function f by starting with the graph of y = x2 ...
 3.3.30: In 1930, graph the function f by starting with the graph of y = x2 ...
 3.3.31: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.32: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.33: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.34: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.35: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.36: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.37: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.38: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.39: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.40: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.41: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.42: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.43: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.44: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.45: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.46: In 31 46, (a) graph each quadratic function by determining whether ...
 3.3.47: In 4752, determine the quadratic function whose graph is given.
 3.3.48: In 4752, determine the quadratic function whose graph is given.
 3.3.49: In 4752, determine the quadratic function whose graph is given.
 3.3.50: In 4752, determine the quadratic function whose graph is given.
 3.3.51: In 4752, determine the quadratic function whose graph is given.
 3.3.52: In 4752, determine the quadratic function whose graph is given.
 3.3.53: In 5360, determine, without graphing, whether the given quadratic f...
 3.3.54: In 5360, determine, without graphing, whether the given quadratic f...
 3.3.55: In 5360, determine, without graphing, whether the given quadratic f...
 3.3.56: In 5360, determine, without graphing, whether the given quadratic f...
 3.3.57: In 5360, determine, without graphing, whether the given quadratic f...
 3.3.58: In 5360, determine, without graphing, whether the given quadratic f...
 3.3.59: In 5360, determine, without graphing, whether the given quadratic f...
 3.3.60: In 5360, determine, without graphing, whether the given quadratic f...
 3.3.61: In 6172, (a) graph each function, (b) determine the domain and the ...
 3.3.62: In 6172, (a) graph each function, (b) determine the domain and the ...
 3.3.63: In 6172, (a) graph each function, (b) determine the domain and the ...
 3.3.64: In 6172, (a) graph each function, (b) determine the domain and the ...
 3.3.65: In 6172, (a) graph each function, (b) determine the domain and the ...
 3.3.66: In 6172, (a) graph each function, (b) determine the domain and the ...
 3.3.67: In 6172, (a) graph each function, (b) determine the domain and the ...
 3.3.68: In 6172, (a) graph each function, (b) determine the domain and the ...
 3.3.69: In 6172, (a) graph each function, (b) determine the domain and the ...
 3.3.70: In 6172, (a) graph each function, (b) determine the domain and the ...
 3.3.71: In 6172, (a) graph each function, (b) determine the domain and the ...
 3.3.72: In 6172, (a) graph each function, (b) determine the domain and the ...
 3.3.73: The graph of the function f1x2 = ax2 + bx + c has vertex at (0, 2) ...
 3.3.74: The graph of the function f1x2 = ax2 + bx + c has vertex at (1, 4) ...
 3.3.75: In 7580, for the given functions f and g, (a) Graph f and g on the ...
 3.3.76: In 7580, for the given functions f and g, (a) Graph f and g on the ...
 3.3.77: In 7580, for the given functions f and g, (a) Graph f and g on the ...
 3.3.78: In 7580, for the given functions f and g, (a) Graph f and g on the ...
 3.3.79: In 7580, for the given functions f and g, (a) Graph f and g on the ...
 3.3.80: In 7580, for the given functions f and g, (a) Graph f and g on the ...
 3.3.81: (a) Find a quadratic function whose xintercepts are 3 and 1 with ...
 3.3.82: (a) Find a quadratic function whose xintercepts are 5 and 3 with ...
 3.3.83: Suppose that f1x2 = x2 + 4x  21. (a) What is the vertex of f ? (b)...
 3.3.84: Suppose that f1x2 = x2 + 2x  8. (a) What is the vertex of f ? (b) ...
 3.3.85: Find the point on the line y = x that is closest to the point (3, 1...
 3.3.86: Find the point on the line y = x + 1 that is closest to the point (...
 3.3.87: Suppose that the manufacturer of a gas clothes dryer has found that...
 3.3.88: The John Deere company has found that the revenue, in dollars, from...
 3.3.89: The marginal cost of a product can be thought of as the cost of pro...
 3.3.90: (See 89.) The marginal cost C (in dollars) of manufacturing x cell ...
 3.3.91: The monthly revenue R achieved by selling x wristwatches is figured...
 3.3.92: The daily revenue R achieved by selling x boxes of candy is figured...
 3.3.93: An accepted relationship between stopping distance, d (in feet), an...
 3.3.94: In the United States, the birthrate B of unmarried women (births pe...
 3.3.95: Find a quadratic function whose xintercepts are 4 and 2 and whose...
 3.3.96: Find a quadratic function whose xintercepts are 1 and 5 and whose...
 3.3.97: Let f1x2 = ax2 + bx + c, where a, b, and c are odd integers. If x i...
 3.3.98: Make up a quadratic function that opens down and has only one xint...
 3.3.99: On one set of coordinate axes, graph the family of parabolas f1x2 =...
 3.3.100: On one set of coordinate axes, graph the family of parabolas f1x2 =...
 3.3.101: State the circumstances that cause the graph of a quadratic functio...
 3.3.102: Why does the graph of a quadratic function open up if a 7 0 and dow...
 3.3.103: Can a quadratic function have a range of ( , )? Justify your answe...
 3.3.104: What are the possibilities for the number of times the graphs of tw...
Solutions for Chapter 3.3: Quadratic Functions and Their Properties
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 3.3: Quadratic Functions and Their Properties
Get Full SolutionsPrecalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3.3: Quadratic Functions and Their Properties includes 104 full stepbystep solutions. Since 104 problems in chapter 3.3: Quadratic Functions and Their Properties have been answered, more than 53504 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

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.)

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

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.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

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

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.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

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.

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

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

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!

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!