EXAMPLE 1 Graph an equation of a parabola SOLUTION STEP 1 Rewrite the equation in standard form. 1818 x = – Write original equation. 1818 Graph x = – y.

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

1 of 7 Pre-Calculus2 Chapter 10 Section 8 Warm up Write the equation in standard form of Write the equation in standard form of Then find the coordinates.

8.2 Graph and Write Equations of Parabolas

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

Table of Contents Parabola - Finding the Equation Recall that the equations for a parabola are given by... Vertical Axis of SymmetryHorizontal Axis of.

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.

Standard 9 Write a quadratic function in vertex form

Find the point(s) of intersection algebraically..

Sullivan Algebra and Trigonometry: Section 10.2 The Parabola

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

EXAMPLE 1 Find the axis of symmetry and the vertex Consider the function y = – 2x x – 7. a. Find the axis of symmetry of the graph of the function.

10.2 Parabolas What you should learn: Goal1 Goal2 Graph and write equations of parabolas. Identify the FOCUS and DIRECTRIX of the parabola Parabolas.

10.2 Parabolas By: L. Keali’i Alicea. Parabolas We have seen parabolas before. Can anyone tell me where? That’s right! Quadratics! Quadratics can take.

What type of conic is each?. Hyperbolas 5.4 (M3)

Section 9-5 Hyperbolas. Objectives I can write equations for hyperbolas I can graph hyperbolas I can Complete the Square to obtain Standard Format of.

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.

EXAMPLE 1 Standardized Test Practice SOLUTION Let ( x 1, y 1 ) = ( –3, 5) and ( x 2, y 2 ) = ( 4, – 1 ). = (4 – (–3)) 2 + (– 1 – 5) 2 = = 85 (

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.

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.

Graphing Quadratic Equations

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.

PARABOLAS GOAL: GRAPH AND EQUATIONS OF PARABOLAS.

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.

Graph an equation of an ellipse

EXAMPLE 1 Graph an equation of a hyperbola Graph 25y 2 – 4x 2 = 100. Identify the vertices, foci, and asymptotes of the hyperbola. SOLUTION STEP 1 Rewrite.

GRAPHING QUADRATIC FUNCTIONS

Advanced Geometry Conic Sections Lesson 3

Vertex form Form: Just like absolute value graphs, you will translate the parent function h is positive, shift right; h is negative, shift left K is positive,

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

The Parabola. Definition of a Parabola A Parabola is the set of all points in a plane that are equidistant from a fixed line (the directrix) and a fixed.

Focus of a Parabola Section 2.3 beginning on page 68.

Focus and Directrix 5-4 English Casbarro Unit 5: Polynomials.

Graph an equation of a hyperbola

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.

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,

Objectives: You will be able to define parametric equations, graph curves parametrically, and solve application problems using parametric equations. Agenda:

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

Writing Equations of Parabolas

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

The Parabola 10.1.

Section 9.1 Parabolas.

Coefficients a, b, and c are coefficients Examples: Find a, b, and c.

Introduction The equation of a quadratic function can be written in several different forms. We have practiced using the standard form of a quadratic function.

2-3: Focus of a Parabola Explore the focus and the directrix of a parabola. Write equations of parabolas.

Parabolas 4.2. Parabolas 4.2 Standard Form of Parabolic Equations Standard Form of Equation Axis of Symmetry Vertex Direction Parabola Opens up or.

2-3: Focus of a Parabola Explore the focus and the directrix of a parabola. Write equations of parabolas.

9.2 Graph & Write Equations of Parabolas

Conic Sections Parabola.

Circles and Parabolas Dr. Shildneck Fall, 2014.

8.4 - Graphing f (x) = a(x − h)2 + k

Parabolas Section

10.2 Parabolas.

9.2 Graph and Write Equations of Parabolas

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 -

Calculate points from this table and plot the points as you go.

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 -

Important Idea Every point on the parabola is the same distance from the focus and the directrix.

Important Idea Every point on the parabola is the same distance from the focus and the directrix.

Presentation transcript:

EXAMPLE 1 Graph an equation of a parabola SOLUTION STEP 1 Rewrite the equation in standard form x = – Write original equation Graph x = – y 2. Identify the focus, directrix, and axis of symmetry. – 8x = y 2 Multiply each side by – 8.

EXAMPLE 1 Graph an equation of a parabola STEP 2 Identify the focus, directrix, and axis of symmetry. The equation has the form y 2 = 4px where p = – 2. The focus is (p, 0), or (– 2, 0). The directrix is x = – p, or x = 2. Because y is squared, the axis of symmetry is the x - axis. STEP 3 Draw the parabola by making a table of values and plotting points. Because p < 0, the parabola opens to the left. So, use only negative x - values.

EXAMPLE 1 Graph an equation of a parabola

EXAMPLE 2 Write an equation of a parabola SOLUTION The graph shows that the vertex is (0, 0) and the directrix is y = – p = for p in the standard form of the equation of a parabola – x 2 = 4py Standard form, vertical axis of symmetry x 2 = 4 ( ) y 3232 Substitute for p 3232 x 2 = 6y Simplify. Write an equation of the parabola shown.

GUIDED PRACTICE for Examples 1, and 2 Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 1. y 2 = –6x SOLUTION STEP 1 Rewrite the equation in standard form. y 2 = 4 (– )x 3 2

GUIDED PRACTICE for Examples 1, and 2 STEP 2 Identify the focus, directrix, and axis of symmetry. The equation has the form y 2 = 4px where p = –. The focus is (p, 0), or (–, 0). The directrix is x = – p, or x =. Because y is squared, the axis of symmetry is the x - axis

GUIDED PRACTICE for Examples 1, and 2 STEP 3 Draw the parabola by making a table of values and plotting points. Because p < 0, the parabola opens to the left. So, use only negative x - values

GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 2. x 2 = 2y SOLUTION

GUIDED PRACTICE for Examples 1 and 2 SOLUTION STEP 1 Rewrite the equation in standard form. Write original equation. – 4y = x 2 Multiply each side by – 4. Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 3. y = – x y = – x

GUIDED PRACTICE for Examples 1 and 2 focus directrixaxis of symmetry x 2 = – 4 0, –1y = 1 Vertical x = 0 equation STEP 2

GUIDED PRACTICE for Examples 1 and 2 STEP 3 Draw the parabola by making a table of values and plotting points. Because p < 0, the parabola opens to the left. So, use only negative y - values. y x

GUIDED PRACTICE for Examples 1 and 2 SOLUTION STEP 1 Rewrite the equation in standard form. Write original equation. 3x = y 2 Multiply each side by 3. Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 4. x = – y x = – y2y2

GUIDED PRACTICE for Examples 1 and 2 focus directrixaxis of symmetry Horizontal y = 0 equation STEP 2 y 2 = 4 x 3 4 0, 3 4 x = – 3 4

GUIDED PRACTICE for Examples 1 and 2 STEP 3 Draw the parabola by making a table of values and plotting points. Because p < 0, the parabola opens to the left. So, use only negative x - values. y x

GUIDED PRACTICE for Examples 1 and 2 Write the standard form of the equation of the parabola with vertex at (0, 0) and the given directrix or focus. 5. Directrix: y = 2 x 2 = 4py Standard form, vertical axis of symmetry x 2 = 4 ( –2)y Substitute –2 for p x 2 = – 8y Simplify. SOLUTION

GUIDED PRACTICE for Examples 1 and 2 Write the standard form of the equation of the parabola with vertex at (0, 0) and the given directrix or focus. 6. Directrix: x = 4 y 2 = 4px Standard form, vertical axis of symmetry y 2 = 4 ( –4)x Substitute –4 for p y 2 = – 16x Simplify. SOLUTION

GUIDED PRACTICE for Examples 1 and 2 Write the standard form of the equation of the parabola with vertex at (0, 0) and the given directrix or focus. 7. Focus: (–2, 0) y 2 = 4px Standard form, vertical axis of symmetry y 2 = 4 ( –2)x Substitute –2 for p y 2 = – 8x Simplify. SOLUTION

GUIDED PRACTICE for Examples 1 and 2 Write the standard form of the equation of the parabola with vertex at (0, 0) and the given directrix or focus. x 2 = 4py Standard form, vertical axis of symmetry x 2 = 4 (3)y Substitute 3 for p x 2 = 12y Simplify. 8. Focus: (0, 3) SOLUTION