is invertible. FOURTH SIX WEEKS 15 D.1.a 422-431, 432-441, 442-452 D.1.b 15.) Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, Students: D.1.c and degenerate conics, from second-degree equations. (Alabama) Given a second degree conic equation, D.1.d D.1.e Example: Graph - 6x + - 12y + 41 = 0 or - 4x + 2y + 5 = 0. x2 y2 y2 Graph parabolas. Graph hyperbolas. a. Formulate equations of conic sections from their determining characteristics. Graph ellipses. (Alabama) Graph circles. Example: Write the equation of an ellipse with center (5, -3), a horizontal major axis Graph degenerate conics. of length 10, and a minor axis of length 4. Given the determining characteristics of a conic section, formulate its equation. 36 36.) (+) Derive the equations of a parabola given a focus and directrix. [G-GPE2] Students: 422-431 Given the focus and directrix of a parabola, Use the distance formula to write an equation for all points which are equidistant from a given focus and directory, Use logical repeated reasoning to generalize to a general point and general directrix, developing the formula for the equation of a parabola, Compare and contrast parabola equations for horizontal and vertical directrices.
is invertible. FOURTH SIX WEEKS 15 D.1.a D.1.b D.1.c D.1.d D.1.e 15.) Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations. (Alabama) Example: Graph x2 - 6x + y2 - 12y + 41 = 0 or y2 - 4x + 2y + 5 = 0. a. Formulate equations of conic sections from their determining characteristics. (Alabama) Example: Write the equation of an ellipse with center (5, -3), a horizontal major axis of length 10, and a minor axis of length 4. Students: Given a second degree conic equation, Graph parabolas. Graph hyperbolas. Graph ellipses. Graph circles. Graph degenerate conics. Given the determining characteristics of a conic section, formulate its equation. 422-431, 432-441, 442-452 36 36.) (+) Derive the equations of a parabola given a focus and directrix. [G-GPE2] Students: Given the focus and directrix of a parabola, Use the distance formula to write an equation for all points which are equidistant from a given focus and directory, Use logical repeated reasoning to generalize to a general point and general directrix, developing the formula for the equation of a parabola, Compare and contrast parabola equations for horizontal and vertical directrices. 422-431