PPT-The Parabola

Unit 5 Conics The parabola is the locus of all points in a plane that are the same distance from a line in the plane the directrix as from a fixed point in the plane the focus Point Focus Point Directrix. http://datapeak.net/mathematics.htm. -. 2 -1 . . 0 . 1 2. y = x. 2. . Archimedes determined that the area of the parabola was . 4/3 . that of the inscribed triangle. Warm Up. 13. 2. . from (0, 2) to (12, 7). Find each distance.. 3. . from the line . y. = –6 to (12, 7). 13. 1. . Given . , . solve for . p. when . c. =. Write the standard equation of a parabola and its axis of symmetry.. Factor: 3x. 2. + 10x + 8. Factor and Solve: 2x. 2. - 7x + 3 = 0. Math I. UNIT QUESTION: What is a quadratic function?. Standard: . MM2A3, MM2A4. Today’s Question:. How do you graph quadratic functions in vertex form?. 5.1 Stretching/Reflecting Quadratic Relations. SQUARE. STRETCH IT. COMPRESS IT. TRIANGLE. STRETCH IT. COMPRESS IT. We can transform the shape of a parabola too:. Transforming Parabolas. y = x. 2. y = 9x. Conic sections will be defined in two different ways in this unit.. The set of points formed by the intersection of a plane and a double-napped cone.. The set of points satisfying certain conditions in relationship to a fixed point and a fixed line or to two fixed points. OTHER VIEW OF CONIC SECTIONS. THE CIRCLE. CONIC SECTION – THE CIRCLE. Equation for a Circle. Standard Form: x² + y² = r². You can determine the equation for a circle by using the distance formula then applying the standard form equation.. 3/31/14. Graphing a Parabola with vertex (. h,k. ). y. 2. – 6y -2x + 8 = 0. X. 2. – 2x – 8y – 7 = 0. Graphing a Parabola with vertex (. h,k. ). Finding the location of the receiver in a Satellite Dish.. Recall…. A quadratic equation is an equation/function of the form f(x) = ax. 2. + . bx. + c. Vertex Form. To facilitate an easier way to graph, we can look at the . vertex form. of a quadratic. Vertex. Coordinate Systems. Dr J Frost (jfrost@tiffin.kingston.sch.uk) . Last modified: . 29. th. August 2015. Conic Sections. In FP1 and FP3, we’ll be examining different types of curves.. All the ones you’ll see can be obtained by taking ‘slices’ of a cone (known as a . La gamme de thé MORPHEE vise toute générations recherchant le sommeil paisible tant désiré et non procuré par tout types de médicaments. Essentiellement composé de feuille de morphine, ce thé vous assurera d’un rétablissement digne d’un voyage sur . Valerie Belew . History of Parabolas . Menaechmus. (380 BC - 320 BC) found the parabola. Apollonius (262 BC - 190 BC) named the parabola. Pappus. (290 - 350) found the focus and . directrix. of the parabola. Pencil, 60/30°, Compass Set-Square & Masking tape. Step 1: Set up and line out page as per specification. Step 2: Locate start point of parabola on the page. Step 3: Using the rectangle method, draw a rectangle using desired measurements. Note that measurements divisible by 5 are easy to work with.. Find each distance.. 3. . from the line . y. = –6 to (12, 7). 13. 1. . Given . , . solve for . p. when . c. =. Write the standard equation of a parabola and its axis of symmetry.. Graph a parabola and identify its focus, directrix, and axis of symmetry.. Parabola in Parallelogram. The coordinates of two points on the parallelogram, . and . , are shown on the diagram. Also shown is the . -coordinate of the minimum point.. The upper dashed line extends the chord .