EXAMPLE 3 Solve a multi-step problem Solar Energy The EuroDish, developed to provide electricity in remote areas, uses a parabolic reflector to concentrate.

Slides:

Advertisements

Similar presentations

Checking an equation for symmetry

Advertisements

Solve a multi-step problem

EXAMPLE 5 Standardized Test Practice How would the graph of the function y = x be affected if the function were changed to y = x 2 + 2? A The graph.

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

Reflective Property of Parabolas

Copyright © 2007 Pearson Education, Inc. Slide 6-2 Chapter 6: Analytic Geometry 6.1Circles and Parabolas 6.2Ellipses and Hyperbolas 6.3Summary of the.

Section 9.3 The Parabola.

Solve an equation with variables on both sides

EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 =

EXAMPLE 2 Using the Cross Products Property = 40.8 m Write original proportion. Cross products property Multiply. 6.8m 6.8 = Divide.

Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.

Math 143 Section 7.3 Parabolas. A parabola is a set of points in a plane that are equidistant from a fixed line, the directrix, and a fixed point, the.

8.2 Graph and Write Equations of Parabolas

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

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

Graph an equation of a parabola

EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by x2x.

EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. The radius is 3 and the center is at the origin. x 2 + y 2 = r 2 x 2 +

Copyright © Cengage Learning. All rights reserved. Conic Sections.

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

Solve a radical equation

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

EXAMPLE 3 Solve a multi-step problem Photography You can take panoramic photographs using a hyperbolic mirror. Light rays heading toward the focus behind.

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 (

1. Graph the function y = 2x. ANSWER

TH EDITION LIAL HORNSBY SCHNEIDER COLLEGE ALGEBRA.

Equations of Parabolas. A parabola is a set of points in a plane that are equidistant from a fixed line, the directrix, and a fixed point, the focus.

Lesson 5.2 AIM: Review of Vertex and Axis of Symmetry.

EXAMPLE 2 Write an equation given a vertex and a co-vertex Write an equation of the ellipse that has a vertex at (0, 4), a co-vertex at (– 3, 0), and center.

Solve an equation using addition EXAMPLE 2 Solve x – 12 = 3. Horizontal format Vertical format x– 12 = 3 Write original equation. x – 12 = 3 Add 12 to.

Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

EXAMPLE 3 Write an equation of a translated parabola

EXAMPLE 2 Checking Solutions Tell whether (7, 6) is a solution of x + 3y = 14. – x + 3y = 14 Write original equation ( 6) = 14 – ? Substitute 7 for.

Use the substitution method

Focus of a Parabola Section 2.3 beginning on page 68.

Today in Precalculus Go over homework Notes: Parabolas –Completing the square –Writing the equation given the graph –Applications Homework.

2.10 Warm Up Multiply the following polynomials. 1. (3p 4 – 5)(2p² + 4) 2. (8n² - 1)(3n² - 4n + 5) 3. (2s + 5)(s² + 3s – 1)

SOLUTION Textiles EXAMPLE 2 Solve a Multi-Step Problem Find the angle measures indicated in the rug design if m 1 = 122. STEP 1 It is given that m 1= 122.

EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. SOLUTION The radius is 3 and the center is at the origin. x 2 + y 2 = r.

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,

10.1 Circles and Parabolas Conic Sections

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

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

Do Now: A parabola has an axis of symmetry y = 3 and passes through (2,1). Find another point that lies on the graph Identify the focus, directrix, and.

Solve a literal equation

Solve an equation by multiplying by a reciprocal

3-2: Solving Systems of Equations using Substitution

Find the surface area of a sphere

3-2: Solving Systems of Equations using Substitution

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

Solving Systems of Equations using Substitution

Unit 2: Day 6 Continue .

Section 9.3 The Parabola.

3-2: Solving Systems of Equations using Substitution

Chapter 6: Analytic Geometry

Chapter 6: Analytic Geometry

Chapter 6: Analytic Geometry

3-2: Solving Systems of Equations using Substitution

Section 9.3 The Parabola.

Parabolas GEO HN CCSS: G.GPE.2

Section 9.3 The Parabola.

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

Presentation transcript:

EXAMPLE 3 Solve a multi-step problem Solar Energy The EuroDish, developed to provide electricity in remote areas, uses a parabolic reflector to concentrate sunlight onto a high-efficiency engine located at the reflector’s focus. The sunlight heats helium to 650°C to power the engine. Write an equation for the EuroDish’s cross section with its vertex at (0, 0). How deep is the dish?

EXAMPLE 3 Solve a multi-step problem SOLUTION STEP 1 Write an equation for the cross section. The engine is at the focus, which is | p | = 4.5 meters from the vertex. Because the focus is above the vertex, p is positive, so p = 4.5. An equation for the cross section of the EuroDish with its vertex at the origin is as follows: x 2 = 4py Standard form, vertical axis of symmetry x 2 = 4(4.5)y Substitute 4.5 for p. x 2 = 18y Simplify.

EXAMPLE 3 Solve a multi-step problem STEP 2 x 2 = 18y Equation for the cross section (4.25) 2 = 18y Substitute 4.25 for p. Solve for y. Find the depth of the EuroDish. The depth is the y - value at the dish’s outside edge. The dish extends = 4.25 meters to either side of the vertex (0, 0), so substitute 4.25 for x in the equation from Step vertex (0, 0), so substitute 4.25 for x in the equation from Step y

EXAMPLE 3 Solve a multi-step problem ANSWER The dish is about 1 meter deep.

GUIDED PRACTICE for Example 3 A parabolic microwave antenna is 16 feet in diameter. Find an equation for the cross section of the antenna with its vertex at the origin and its focus 10 feet to the right of its vertex. Then find the antenna’s depth. 9. Microwaves

GUIDED PRACTICE for Example 3 SOLUTION STEP 1 Write an equation for the cross section. Because the focus is right of the vertex, so p = 10. An equation for the cross section of the Antenna with its vertex at the origin is as follows: y 2 = 4px Standard form, vertical axis of symmetry y 2 = 4(10)x Substitute 4.5 for p. y 2 = 40x Simplify.

GUIDED PRACTICE for Example 3 STEP 2 y 2 = 40x Equation for the cross section (8) 2 = 40x Substitute 8 for p. Solve for x. Find the depth of the antenna. The depth is the x - value at the antenna outside edge. The antenna extends = 8 feet to either side of the vertex (0,0), so substitute 8 for y in the equation from Step x ANSWER The antenna is 1.6 ft deep.