Warm-up!!. CCGPS Geometry Day 60 (11-5-13) UNIT QUESTION: How are the equations of circles and parabolas derived? Standard: MCC9-12..A.REI.7, G.GPE.1,2.

Slides:

Advertisements

Similar presentations

Parabola Conic section.

Advertisements

Conics D.Wetzel 2009.

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.

9.2 Parabola Hyperbola/Parabola Quiz: FRIDAY Concis Test: March 26.

Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) focus directrix.

M3U4D8 Warm Up Find the vertex using completing the square: 2x2 + 8x – 12 = 0 x2 + 4x – 6 = 0 x2 + 4x = 6 x2 + 4x +__ = 6 + __ (x + )2 = (x + 2) 2 –

Introduction A theorem is statement that is shown to be true. Some important theorems have names, such as the Pythagorean Theorem, but many theorems do.

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.

EXAMPLE 1 Graph an equation of a parabola SOLUTION STEP 1 Rewrite the equation in standard form x = – Write original equation Graph x = – y.

Parabolas Date: ____________.

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

Section 9.1 Conics.

Graph an equation of a parabola

Parabolas Section 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.

Parabolas Definitions Parabola – set of all points equidistant from a fixed line (directrix) and a fixed point (focus) Vertex – midpoint of segment from.

CCGPS GEOMETRY UNIT QUESTION: How are the equations of circles and parabolas derived? Standard: MCC9-12..A.REI.7, G.GPE.1,2 and 4 Today’s Question: How.

Sullivan Algebra and Trigonometry: Section 10.2 The Parabola

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

Conic Sections Parabola. Conic Sections - Parabola The intersection of a plane with one nappe of the cone is a parabola.

Unit 1 – Conic Sections Section 1.3 – The Parabola Calculator Required Vertex: (h, k) Opens Left/RightOpens Up/Down Vertex: (h, k) Focus: Directrix: Axis.

ALGEBRA 2 Write an equation for a graph that is the set of all points in the plane that are equidistant from point F(0, 1) and the line y = –1. You need.

10.2 Parabolas JMerrill, Review—What are Conics Conics are formed by the intersection of a plane and a double-napped cone. There are 4 basic conic.

Circles Circles/Ellipse Quiz: March 9 Midterm: March 11 (next Thursday)

Conics A conic section is a graph that results from the intersection of a plane and a double cone.

10.2 Parabolas Where is the focus and directrix compared to the vertex? How do you know what direction a parabola opens? How do you write the equation.

6 minutes Warm-Up For each parabola, find an equation for the axis of symmetry and the coordinates of the vertex. State whether the parabola opens up.

9.2 Notes – Parabolas.

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,

TH EDITION LIAL HORNSBY SCHNEIDER COLLEGE ALGEBRA.

Warmup Alg 2 19 Apr Agenda Don't forget about resources on mrwaddell.net Section 9.2: Parabolas again! Non-Zero Vertex Completing the Square with.

Chapter : parabolas 8-2 : ellipse 8-3 : hyperbolas 8-4 : translating and rotating conics 8-5 : writing conics in polar form 8-6 : 3-D coordinate.

April 18, 2012 Conic Sections Intro - Parabola Warm-up: Write the quadratic equation in vertex form and identify the vertex. 1.y = x 2 – 6x y =

Advanced Geometry Conic Sections Lesson 3

Conic Sections The Parabola. Introduction Consider a ___________ being intersected with a __________.

CCGPS GEOMETRY UNIT QUESTION: How are the equations of circles and parabolas derived? Standard: MCC9-12..A.REI.7, G.GPE.1,2 and 4 Today’s Question: How.

Find the distance between (-4, 2) and (6, -3). Find the midpoint of the segment connecting (3, -2) and (4, 5).

Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)

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.

Equation of a Parabola. Do Now  What is the distance formula?  How do you measure the distance from a point to a line?

INTRO TO CONIC SECTIONS. IT ALL DEPENDS ON HOW YOU SLICE IT! Start with a cone:

Warm-Up Exercises 1. Identify the axis of symmetry for the graph of y = 3x 2. ANSWER x = 0 2. Identify the vertex of the graph of y = 3x 2. ANSWER (0,

11.3 PARABOLAS Directrix (L): A line in a plane.

8.2 Parabolas 12/15/09.

The Parabola 10.1.

Section 9.1 Parabolas.

Conics A conic section is a graph that results from the intersection of a plane and a double cone.

Conics A conic section is a graph that results from the intersection of a plane and a double cone.

Unit 2: Day 6 Continue .

Warmup What is the radius and center of this circle?

Section 10.1 The Parabola Copyright ©2013, 2009, 2006, 2005 Pearson Education, Inc.

Circles and Parabolas Dr. Shildneck Fall, 2014.

Parabolas Section

10.2 Parabolas.

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.

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

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 -

Warm-up: 1) Find the standard form of the equation of the parabola given: the vertex is (3, 1) and focus is (5, 1) 2) Graph a sketch of (x – 3)2 = 16y.

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 -

Five-Minute Check (over Lesson 9–7) Mathematical Practices Then/Now

L10-2 Obj: Students will be able to find equations for parabolas

Presentation transcript:

Warm-up!!

CCGPS Geometry Day 60 ( ) UNIT QUESTION: How are the equations of circles and parabolas derived? Standard: MCC9-12..A.REI.7, G.GPE.1,2 and 4 Today’s Question: How do we graph a parabola from a given equation in standard form? Standard: MCC9-12..G.GPE.2

Parabolas Parabolas

Parabolas Parabola: the set of points in a plane that are the same distance from a given point called the focus and a given line called the directrix. Directrix The light source is the Focus The cross section of a headlight is an example of a parabola...

Here are some other applications of the parabola...

Directrix Focus d1d1 d1d1 d2d2 d2d2 d3d3 d3d3 Also, notice that the distance from the focus to any point on the parabola is equal to the distance from that point to the directrix... We can determine the coordinates of the focus, and the equation of the directrix, given the equation of the parabola.... Vertex Notice that the vertex is located at the midpoint between the focus and the directrix...

Standard Equation of a Parabola: (Vertex at the origin) EquationFocusDirectrix x 2 = 4py (0, p)y = –p EquationFocusDirectrix y 2 = 4px (p, 0)x = –p (If the x term is squared, the parabola is up or down) (If the y term is squared, the parabola is left or right)

Tell whether the parabola opens up down, left, or right. down right left

Find the focus and equation of the directrix. Then sketch the graph. Opens right

Find the focus and equation of the directrix. Then sketch the graph. Opens up

Find the focus and equation of the directrix. Then sketch the graph. Opens down

Find the focus and equation of the directrix. Then sketch the graph. Opens left

Example 5: Determine the focus and directrix of the parabola (y – 2) 2 = -16 (x - 5) : Direction: Vertex: Focus: Directrix:

Example 6: Determine the focus and directrix of the parabola (x – 6) 2 = 8(y + 3) : Direction: Vertex: Focus: Directrix:

7. Write the equation in standard form by completing the square. State the VERTEX.

8. Write the equation in standard form by completing the square. State the VERTEX. You TRY!!