Mathematics & Statistics Texas Tech University Kent Pearce Department of Mathematics and Statistics Texas Tech University Lubbock, Texas 79409-1042 Voice: (806)742-2566 x 226 FAX: (806)742-1112 Email: kent.pearce@ttu.edu

 Math 1350 Analytical Geometry Fall 2014 Riddle Analytical Geometry Brooks/Cole

Review Exam III

 Section Content Suggested Problems Section 6.1 Translation of conic sections Equations of translation x = x' + h y = y' + k Standard forms for conic sections Parabola Type I: Axis of symmetry parallel to x-axis Type II: Axis of symmetry parallel to y-axis Ellipse Type I: Major axis parallel to x-axis Type II: Major axis parallel to y-axis Hyperbola Type I: Transverse axis parallel to x-axis Type II: Transverse axis parallel to y-axis 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 θ = 45° Case A ≠ C tan 2θ = B/(A-C) Reference triange for angle 2θ Trig half angle formulas for cos θ and sin θ Discrimant B2 - 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 y-axis Symmetry wrt x-axis Symmetry wrt origin Symmetry wrt line y=x Intercepts x-axis Roots of factors of numerator y-axis Value at x = 0 Page 232: 1-4, 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 (x-a)n Odd power of n n=1 n=3, 5, 7, . . . 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 y = 0 Case Degree Numerator = Degree Denominator y = a_n/b_n Case Degree Numerator > Degree Denominator None 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 (x-axis) 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 y2 = p(x) Graph auxillary function z = p(x) Graph y = ± square root (z) Page 273: 1, 5, 7, 11, 15

Home | Vita | Pre-Prints | Courses | Pre Lims | Links | Jokes

Comments maybe be mailed to: kent.pearce@ttu.edu