Parabola Last Updated: October 11, 2005.

Slides:

Advertisements

Similar presentations

Objectives Write the standard equation of a parabola and its axis of symmetry. Graph a parabola and identify its focus, directrix, and axis of symmetry.

Advertisements

What do we know about parabolas?. Conic Slice Algebraic Definition Parabola: For a given point, called the focus, and a given line not through the focus,

Section 7.1 – Conics Conics – curves that are created by the intersection of a plane and a right circular cone.

Recall that the equations for a parabola are given by ...

Table of Contents Parabola - Definition and Equations Consider a fixed point F in the plane which we shall call the focus, and a line which we will call.

& & & Formulas.

Warm Up Parabolas (day two) Objective: To translate equations into vertex form and graph parabolas from that form To identify the focus, vertex,

10.2 The Parabola. A parabola is defined as the locus of all points in a given plane that are the same distance from a fixed point, called the focus,

9.2 THE PARABOLA. A parabola is defined as the collection of all points P in the plane that are the same distance from a fixed point F as they are from.

10.2 The Parabola. A parabola is defined as the collection of all points P in the plane that are the same distance from a fixed point F as they are from.

“Backwards” Parabolas Today you will write the equation of a parabola given defining characteristics or the graph.

Section 9.3 The Parabola. Finally, something familiar! The parabola is oft discussed in MTH 112, as it is the graph of a quadratic function: Does look.

Algebra II Section 8-2 Parabolas (the dreaded lesson)

Advanced Geometry Conic Sections Lesson 3

Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School

Jeff Bivin -- LZHS Last Updated: March 11, 2008 Section 10.2.

Graphing Parabolas Using the Vertex Axis of Symmetry & y-Intercept By: Jeffrey Bivin Lake Zurich High School

Parabola  The set of all points that are equidistant from a given point (focus) and a given line (directrix).

March 19 th copyright2009merrydavidson Conic sections.

Conics: Parabolas. Parabolas: The set of all points equidistant from a fixed line called the directrix and a fixed point called the focus. The vertex.

10.2 Parabolas. Objective To determine the relationship between the equation of a parabola and its focus, directrix, vertex, and axis of symmetry. To.

Section 10.2 The Parabola. Find an equation of the parabola with vertex at (0, 0) and focus at (3, 0). Graph the equation. Figure 5.

Conics Name the vertex and the distance from the vertex to the focus of the equation (y+4) 2 = -16(x-1) Question:

PARABOLAS Topic 7.2.

Section 10.2 – The Parabola Opens Left/Right Opens Up/Down

Writing Equations of Parabolas

10.5 Parabolas Objective: Use and determine the standard and general forms of the equations of a parabolas. Graph parabolas.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

10.1 Parabolas.

Solving Quadratics by Completing the Square & Quadratic Formula

Ch10.2 and additional material

Daily Warm Up Determine the vertex and axis of symmetry:

Parabola (Left\Right) Hyperbola (Left Right)

Graph and Write Equations of Parabolas

Worksheet Key 11/28/2018 9:51 AM 9.2: Parabolas.

Lake Zurich High School

This presentation was written by Rebecca Hoffman

Unit 2: Day 6 Continue .

Day 137 – Equation of a parabola 2

Warmup What is the radius and center of this circle?

PARABOLAS Topic 7.2.

Section 9.3 The Parabola.

Conic Sections Parabola.

Focus of a Parabola Section 2.3.

Parabolas Objective: Be able to identify the vertex, focus and directrix of a parabola and create an equation for a parabola. Thinking Skill: Explicitly.

Parabolas Section

Lake Zurich High School

Hyperbola Last Updated: October 11, 2005 Jeff Bivin -- LZHS.

Analyzing the Parabola

Ellipse Last Updated: October 11, 2005.

Lake Zurich High School

Warm-Up 1. Find the distance between (3, -3) and (-1, 5)

Write an equation of a parabola with a vertex at the origin and a focus at (–2, 0). [Default] [MC Any] [MC All]

Section 7.2 The Parabola Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Section 9.3 The Parabola.

Section 9.3 The Parabola.

Section 11.6 – Conic Sections

Intro to Conic Sections

5.1 Parabolas a set of points whose distance to a fixed point (focus) equals it’s distance to a fixed line (directrix) A Parabola is -

Graphing Parabolas Without T-charts!.

Conic Sections - Parabolas

5.1 Parabolas a set of points whose distance to a fixed point (focus) equals it’s distance to a fixed line (directrix) A Parabola is -

Parabolas a set of points whose distance to a fixed point (focus) equals it’s distance to a fixed line (directrix) A Parabola is -

CONIC SECTIONS.

Objectives & HW Students will be able to identify vertex, focus, directrix, axis of symmetry, opening and equations of a parabola. HW: p. 403: all.

Circle Last Updated: October 11, 2005.

Chapter 7 Analyzing Conic Sections

10.2 Parabolas Algebra 2.

Presentation transcript:

parabola Last Updated: October 11, 2005

Parabola focus directrix The set of all points that are equidistant from a given point (focus) and a given line (directrix). focus directrix Jeff Bivin -- LZHS

Distance between focus and vertex = p Parabola Distance between focus and vertex = p p p Distance between vertex and directrix = p Jeff Bivin -- LZHS

Parabola The line segment through the focus perpendicular to the axis of symmetry with endpoints on the parabola is called the Latus Rectum (LR) 4p 2p 2p p 2p p Length of the LR = 4p Jeff Bivin -- LZHS

Graph the following parabola y = 3x2 + 24x + 53 y = 3(x2 + 8x ) + 53 3●(4)2 = 48 y + 48 = 3(x2 + 8x + (4)2) + 53 y = 3(x2 + 8x + (4)2) + 53 - 48 y = 3(x + 4)2 + 5 x + 4 = 0 Axis of symmetry: x = -4 Vertex: (-4, 5) Jeff Bivin -- LZHS

Graph the following parabola y = 3(x + 4)2 + 5 Axis of symmetry: x = -4 Vertex: (-4, 5) Jeff Bivin -- LZHS

Graph the following parabola y = 3(x + 4)2 + 5 x = - 4 Axis of symmetry: x = -4 Vertex: (-4, 5) p = 1/4a = 1/(4●3) = 1/12 Focus: (-4 , 5 + 1/12) (- 4, 5) Directrix: y = 5 – 1/12 Length of LR: 4p = 4(1/12) = 1/3 Jeff Bivin -- LZHS

Graph the following parabola y = -2x2 + 12x + 11 y = -2(x2 - 6x ) + 11 -2●(-3)2 = -18 y - 18 = -2(x2 - 6x + (-3)2) + 11 y = -2(x2 - 6x + (-3)2) + 11 + 18 y = -2(x - 3)2 + 29 x - 3 = 0 Axis of symmetry: x = 3 Vertex: (3, 29) Jeff Bivin -- LZHS

Graph the following parabola y = -2(x - 3)2 + 29 Axis of symmetry: x = 3 Vertex: (3, 29) Jeff Bivin -- LZHS

Graph the following parabola y = -2(x - 3)2 + 29 Axis of symmetry: x = 3 (3, 29) Vertex: (3, 29) p = 1/4a = 1/(4●(-2)) = -1/8 Focus: (3 , 29 - 1/8) Directrix: y = 29 + 1/8 x = 3 Length of LR: 4p = 4(1/8) = 1/2 Jeff Bivin -- LZHS

Graph the following parabola x = y2 + 10y + 8 x = (y2 + 10y ) + 8 (5)2 = 25 x + 25 = (y2 + 10y + (5)2) + 8 x = (y2 + 10y + (5)2) + 8 - 25 x = (y + 5)2 - 17 y + 5 = 0 Axis of symmetry: y = -5 Vertex: (-17, -5) Jeff Bivin -- LZHS

Graph the following parabola x = (y + 5)2 - 17 Axis of symmetry: y = -5 Vertex: (-17, -5) Jeff Bivin -- LZHS

Graph the following parabola x = (y + 5)2 - 17 Axis of symmetry: y = -5 Vertex: (-17, -5) (-17, -5) y = -5 p = 1/4a = 1/(4●1) = 1/4 Focus: (-17+1/4 , -5) Directrix: x = -17 - 1/4 Length of LR: 4p = 4(1/4) = 1 Jeff Bivin -- LZHS

Graph the following parabola x = -2y2 - 8y - 1 x = -2(y2 + 4y ) - 1 -2(2)2 = -8 x - 8 = -2(y2 + 4y + (2)2) - 1 x = -2(y2 + 4y + (2)2) - 1 + 8 x = -2(y + 2)2 + 7 y + 2 = 0 Axis of symmetry: y = -2 Vertex: (7, -2) Jeff Bivin -- LZHS

Graph the following parabola x = -2(y + 2)2 + 7 Axis of symmetry: y = -2 Vertex: (7, -2) Jeff Bivin -- LZHS

Graph the following parabola x = -2(y + 2)2 + 7 Axis of symmetry: y = -2 Vertex: (7, -2) focus (7, -2) y = -2 p = 1/4a = 1/(4●(-2)) = -1/8 Focus: (7-1/8 , -2) Directrix: x = 7 + 1/8 Length of LR: 4p = 4(1/8) = 1/2 Jeff Bivin -- LZHS

Graph the following parabola y = 5x2 - 30x + 46 y = 5(x2 - 6x ) + 46 5●(-3)2 = 45 y + 45 = 5(x2 - 6x + (-3)2) + 46 y = 5(x2 - 6x + (-3)2) + 46 - 45 y = 5(x - 3)2 + 1 x - 3 = 0 Axis of symmetry: x = 3 Vertex: (3, 1) Jeff Bivin -- LZHS

Graph the following parabola y = 5(x - 3)2 + 1 Axis of symmetry: x = 3 Vertex: (3, 1) Jeff Bivin -- LZHS

Graph the following parabola y = 5(x - 3)2 + 1 x = 3 Axis of symmetry: x = 3 Vertex: (3, 1) p = 1/4a = 1/(4●5) = 1/20 Focus: (3 , 1 + 1/20) (3, 1) Directrix: y = 1 – 1/20 Length of LR: 4p = 4(1/20) = 1/5 Jeff Bivin -- LZHS

Graph the following parabola x = y2 - 4y + 11 x = (y2 - 8y ) + 11 x + 8 = (y2 - 8y + (-4)2) + 11 x = (y2 - 8y + (-4)2) + 11 - 8 x = (y - 4)2 + 3 y - 4 = 0 Axis of symmetry: y = 4 Vertex: (3, 4) Jeff Bivin -- LZHS

Graph the following parabola x = (y - 4)2 + 3 Axis of symmetry: y = 4 Vertex: (3, 4) (3, 4) y = 4 p = Focus: (3+1/2 , 4) Directrix: x = 3 – 1/2 Length of LR: 4p = 4(1/2) = 2 Jeff Bivin -- LZHS

Some Web Sites http://www.xahlee.org/SpecialPlaneCurves_dir/Parabola_dir/parabolaReflect.mov Jeff Bivin -- LZHS

That's All Folks