PPT-Conics Parabolas Definition - a parabola is the set of all points equal distance from

Parabolas are shaped like a U or C Parabolas Equations yk ax h 2 opens up if a gt 0 opens down if a lt 0 xh ay k 2 opens right if a gt 0 opens left if a lt 0. p = 4k – 1 asymmetry theorem . for quadratic residues . by Jim Adams . Sources. Part I: Mathematics – Number Theory item 2A in www.jimhadams.com.. Part II: Mathematics – Number Theory item 2B.. Date: ____________. Parabolas. Parabola—Set of all points in a plane that are the same distance from a given point called the focus and a given line called the . directrix. .. Vertex. Focus. Directrix. We already know A LOT about parabolas. 2 forms (standard and vertex). How to find Vertex (. h,k. ) or (-b/2a). Axis of Symmetry. Characteristics. Many ways to solve their equations. Solutions are x intercepts. Section 2.3 beginning on page 68. The Big Ideas. In this section we will learn about…. T. he focus and the . directrix. of a parabola. Writing equations for parabolas using the focus, the . directrix. 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.. 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. Holt Algebra 2. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Algebra 2. Warm Up. 13. 2. . from (0, 2) to (12, 7). Find each distance.. 3. . from the line . y. = –6 to (12, 7). 13. 1. . 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 . Garrett . Delk. gdelk71687@csu.fullerton.edu. Department of Mathematics. CSU Fullerton. Presented at . 2013 CMC Conference. Palm Springs, CA. Parabolas and Quadratic Equations. Agenda. Welcome. CCSS. Parabolas. The graph of a quadratic equation. Comprised of several parts. Vertex. Axis of Symmetry. X-. interceptS. (maybe?). Y – intercept . Axis of Symmetry . The central line that splits the middle of the parabola. GeoGebra. Ann . Schnurbusch. Southeast Missouri State University. Occurrence of the Conics. http://britton.disted.camosun.bc.ca/jbconics.htm. (All general info about conics is from this website.). Mathematicians have a habit of studying, just for the fun of it, things that seem utterly useless; then centuries later their studies turn out to have enormous scientific value.  There is no better example of this than the work done by the ancient Greeks on the curves known as the conics: the ellipse, the parabola, and the hyperbola. They were first studied by one of Plato's pupils. No important scientific applications were found for them until the 17th century, when . 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.. Parametric Equations. 6. .1 . Introduction. The General Quadratic Equation in x and y has the form:. Where A, B, C, D, E, F are . constants.. The graphs of these equations are called . Conic Sections.