Section

Content

Suggested Problems

Section 6.1

 Translation of conic sections
 Equations of translation
 Standard forms for conic sections
 Parabola
 Type I: Axis of symmetry parallel to xaxis
 Type II: Axis of symmetry parallel to yaxis
 Ellipse
 Type I: Major axis parallel to xaxis
 Type II: Major axis parallel to yaxis
 Hyperbola
 Type I: Transverse axis parallel to xaxis
 Type II: Transverse axis parallel to yaxis

Page 198: 7, 8, 9, 10, 11, 12, 21, 22, 23, 25

Section 6.3

 Equations of rotation
 x = x' cos θ  y' sin θ
 y = x' sin &theta' + y' cos &theta'
 Transform Quadratic Equation by Rotation

Page 211: 5, 7, 9

Section 6.4

 General second order equation
 Rotate Equation to Eliminate xy term
 Case A = C
 Case A ≠ C
 tan 2θ = B/(AC)
 Reference triange for angle 2θ
 Trig half angle formulas for cos θ and sin θ
 Discrimant B^{2}  4AC

Page 220: 1, 2, 4, 5, 9

Section 7.1

 Definition of Symmetry wrt Line
 Definition of Symmetry wrt Point
 Tests for Symmetry
 Symmetry wrt yaxis
 Symmetry wrt xaxis
 Symmetry wrt origin
 Symmetry wrt line y=x
 Intercepts
 xaxis
 Roots of factors of numerator
 yaxis

Page 232: 14, 11, 13, 17, 19, 21, 23, 27, 28

Section 7.2

 Sketching Polynomial Equations
 Fundamental Theorem of Algebra
 Behavior of Graphs near Intercepts
 Factors of Form (xa)^{n}
 Odd power of n
 Even power of n
 End Behavior
 Sketching Graph
 Symmetry
 Intercepts
 Behavior of Graphs near Intercepts
 End Behavior

Page 243: 1, 5, 9, 13, 27, 28, 29

Section 7.3

 Rational Functions
 Asymptotes
 Vertical
 Roots of factors of denominator
 Horizonatal
 Case Degree Numerator < Degree Denominator
 Case Degree Numerator = Degree Denominator
 Case Degree Numerator > Degree Denominator
 Slant
 Degree Numerator = Degree Denominator + 1
 Divide Numerator by Denominator Longhand

Page 255: 1, 3, 9, 11, 13, 15, 17

Section 7.4

 Sketching the Graphs of Rational Functions
 Symmetry
 Intercepts
 Vertical Asymptotes
 Horizonatal Asymptotes
 Slant Asymptotes
 Interval (xaxis) of Constant Sign

Page 264: 1, 7, 13, 15, 16, 17, 19, 20

Section 7.5

 Equations with Radicals
 Domain Restrictions
 Graph y = square root (p(x))
 Graph auxillary function z = p(x)
 Graph y = square root (z)
 Graph y^{2} = p(x)
 Graph auxillary function z = p(x)
 Graph y = ± square root (z)

Page 273: 1, 5, 7, 11, 15
