5 3 Solving Quadratic Equations By Graphing And Factoring-Books Pdf

5 3 Solving Quadratic Equations by Graphing and Factoring
17 Nov 2019 | 69 views | 0 downloads | 5 Pages | 902.61 KB

Share Pdf : 5 3 Solving Quadratic Equations By Graphing And Factoring

Download and Preview : 5 3 Solving Quadratic Equations By Graphing And Factoring


Report CopyRight/DMCA Form For : 5 3 Solving Quadratic Equations By Graphing And Factoring



Transcription

Find the zeros of f x x 2 2x 3 by using a graph and table . Method 2 Use a calculator , Enter y x 2 2x 3 into a graphing calculator . Both the table and the graph show that y 0 at x 3 and x 1 . These are the zeros of the function , 1 Find the zeros of g x x 2 2x 3 by using a graph and. You can also find zeros by using algebra For example to find the zeros of. Functions have zeros f x x 2 2x 3 you can set the function equal to zero The solutions to. or x intercepts the related equation x 2 2x 3 0 represent the zeros of the function . Equations have, The solutions to a quadratic equation of the form ax 2 bx c 0 are roots The. solutions or roots , roots of an equation are the values of the variable that make the equation true . You can find the roots of some quadratic equations by factoring and applying the. Zero Product Property , Zero Product Property, For all real numbers a and b .
WORDS NUMBERS ALGEBRA, If the product of two quantities 3 0 0 If ab 0 then a 0. equals zero at least one of the 0 4 0 or b 0 , quantities equals zero . EXAMPLE 2 Finding Zeros by Factoring, Find the zeros of each function by factoring . A f x x 2 8x 12, x 2 8x 12 0 Set the function equal to 0 . x 2 x 6 0 Factor Find factors of 12 that add to 8 . x 2 0 or x 6 0 Apply the Zero Product Property , x 2 or x 6 Solve each equation .
x 2 8x 12 0, x 2, 8x 12 0, , Substitute each, 2 2 8 2 12 0 6 8 6 12 0. 2 value into, 4 16 12 0 36 48 12 0 the original, 0 0 0 0 . 334 Chapter 5 Quadratic Functions, a207se c05l03 0333 0340 indd 334 12 14 05 1 50 10 PM. Find the zeros of each function by factoring , B g x 3x 2 12x. 3x 2 12x 0 Set the function equal to 0 , 3x x 4 0 Factor The GCF is 3x .
3x 0 or x 4 0 Apply the Zero Product Property , x 0 or x 4 Solve each equation . Check Check algebraically and by graphing , 3x 2 12x 0. 3x 2 12x 0, x x , 3 0 12 0 0, 3 4 12 4 0, 0 0 0 48 48 0 . Find the zeros of each function by factoring , 2a f x x 2 5x 6 2b g x x 2 8x. Any object that is thrown or launched into the air such as a baseball basketball . or soccer ball is a projectile The general function that approximates the height h. in feet of a projectile on Earth after t seconds is given below . Constant due to Earth s Initial vertical velocity Initial height. gravity in ft s2 in ft s at t 0 in ft at t 0 , Note that this model has limitations because it does not account for air.
resistance wind and other real world factors , EXAMPLE 3 Sports Application. A soccer ball is kicked from ground level with an initial vertical velocity of. 32 ft s After how many seconds will the ball hit the ground . h t 16t 2 v 0t h 0 Write the general projectile function . h t 16t 32t 0, Substitute 32 for v 0 and 0 for h 0 . The ball will hit the ground when its height is zero . 16t 2 32t 0 Set h t equal to 0 , 16t t 2 0 Factor The GCF is 16t . 16t 0 or t 2 0 Apply the Zero Product Property , t 0 or t 2 Solve each equation . The ball will hit the ground in 2 seconds , Notice that the height is also zero when.
t 0 the instant that the ball is kicked , Check The graph of the function. h t 16t 2 32t shows its , zeros at 0 and 2 , 5 3 Solving Quadratic Equations by Graphing and Factoring 335. a207se c05l03 0333 0340 indd 335 12 14 05 1 50 13 PM. 3 A football is kicked from ground level with an initial vertical. velocity of 48 ft s How long is the ball in the air . Quadratic expressions can have one two or three terms such as 16t 2 . 16t 2 25t or 16t 2 25t 6 Quadratic expressions with two terms are. binomials Quadratic expressions with three terms are trinomials Some. quadratic expressions with perfect squares have special factoring rules . Special Products and Factors, Difference of Two Squares Perfect Square Trinomial. a 2 2ab b 2 a b , a 2 b 2 a b a b , a 2 2ab b 2 a b . EXAMPLE 4 Finding Roots by Using Special Factors, Find the roots of each equation by factoring .
A 9x 2 1, 9x 2 1 0 Rewrite in standard form , 3x 1 0. 2 2, Write the left side as a 2 b 2 , 3x 1 3x 1 0 Factor the difference of squares . 3x 1 0 or 3x 1 0 Apply the Zero Product Property . 1 or x , x 1 Solve each equation , 3 3, Check Graph the related function. f x 9x 2 1 on a graphing, calculator The function appears to x x. have zeros at 13 and 13 , B 40x 8x 2 50, A quadratic equation 8x 2 40x 50 0 Rewrite in standard form .
can have two roots, that are equal such 2 4x 20x 25 0. Factor The GCF is 2 , as x 52 and x 52 4x 2 20x 25 0 Divide both sides by 2 . Two equal roots are, sometimes called a 2x 2 2x 5 5 0. 2 2, Write the left side as a 2 2ab b 2 , double root 2x 5 2 0 Factor the perfect square trinomial a b . 2x 5 0 or 2x 5 0 Apply the Zero Product Property . x or x 5, Solve each equation , 2 2, 5 into the original equation .
Check Substitute the root , 40x 8x 50, , 100 100 . Find the roots of each equation by factoring , 4a x 2 4x 4 4b 25x 2 9. 336 Chapter 5 Quadratic Functions, a207se c05l03 0333 0340 indd 336 12 14 05 1 50 15 PM. If you know the zeros of a function you can work backward to write a rule. for the function , EXAMPLE 5 Using Zeros to Write Function Rules. Write a quadratic function in standard form with zeros 2 and 1 . x 2 or x 1 Write the zeros as solutions for two equations . x 2 0 or x 1 0 Rewrite each equation so that it equals 0 . x 2 x 1 0 Apply the converse of the Zero Product, Property to write a product that equals 0 .
x2 x 2 0 Multiply the binomials , f x x x 2, Replace 0 with f x . Check Graph the function, f x x 2 x 2 on a, , calculator The graph shows. the original zeros of 2 and 1 , 5 Write a quadratic function in standard form with. zeros 5 and 5 , Note that there are many quadratic functions x. with the same zeros For example the functions, f x x 2 x 2 g x x 2 x 2 and.
h x 2x 2 2x 4 all have zeros at 2 and 1 , THINK AND DISCUSS. 1 Describe the zeros of a function whose terms form a perfect square. trinomial , 2 Compare the x and y intercepts of a quadratic function with those of a. linear function , 3 Explain how a table can be used to find zeros of a function . 4 GET ORGANIZED Copy and complete the graphic organizer In each. box give information about special products and factors . i i i , vvi i Vi v , i , i viV i , , 5 3 Solving Quadratic Equations by Graphing and Factoring 337. a207se c05l03 0333 0340 indd 337 12 14 05 1 50 17 PM.


Related Books

9.2 Solving Quadratic Equations by Graphing

9 2 Solving Quadratic Equations by Graphing

Solving Quadratic Equations by Graphing A quadratic equation is a nonlinear equation that can be written in the standard form ax2 + bx + c = 0, where a ? 0. In Chapter 7, you solved quadratic equations by factoring. You can also solve quadratic equations by graphing. Solving a Quadratic Equation: Two Real Solutions Solve x2 + 2x = 3 by ...

Offer Date: - eForms

Offer Date eForms

(3) termination of this Agreement due to the default of Seller; or (4) termination of this Agreement in accordance with a specific right to terminate set forth in the Agreement. Otherwise, the earnest money shall be applied towards the purchase price of the Property at

BEST PRACTICES FOR MANAGING VIDEO WORKFLOWS

BEST PRACTICES FOR MANAGING VIDEO WORKFLOWS

This ebook will share best practices from these companies and detail how and why they selected LTO technology and LTFS-based solutions. How LTO Technology and LTFS Manage Every Stage of Content Creation/Management The combination of LTO technology and LTFS improves workflows for each of the four key areas in this industry: 1. Production.

MSC 47D09 DOI: 10.14529/mmp190411 NUMERICAL RESEARCH OF ...

MSC 47D09 DOI 10 14529 mmp190411 NUMERICAL RESEARCH OF

MSC 47D09 DOI: 10.14529/mmp190411 NUMERICAL RESEARCH OF THE MATHEMATICAL MODEL FOR TRAFFIC FLOW A.S. Konkina, South Ural State University, Chelyabinsk, Russian Federation,

British Standard - Tianjin Wellmade Scaffold Co., Ltd

British Standard Tianjin Wellmade Scaffold Co Ltd

in tubular scaffolding and false-work. Recommendations for the design of tubular scaffolding structures are given in BS 5973 and BS 5974. This standard was previously published as Part 1 of BS 1139:1982 which also contained specifications for aluminium scaffold tube. With the exception of

Transistors 101 - Adafruit Industries

Transistors 101 Adafruit Industries

A transistor will act linearly if the base-emitter current is within a specified range (depending on the model of transistor). That means that the collector-emitter current will be some multiple of the base-emitter current. That multiplier is called the transistor's gain. For example, the gain of a 2N3904 (a very common small transistor) is ...

Enhanced Long-Term Care Home Renewal Strategy

Enhanced Long Term Care Home Renewal Strategy

Enhanced Long-Term Care Home Renewal Strategy Survey ... The Construction Funding Subsidy is a per diem funding intended to support construction

Government Travel & Reimbursement Procedures SOP

Government Travel amp Reimbursement Procedures SOP

Government Travel & Reimbursement Procedures SOP ... is less than 12 hours and no per diem is ... Please contact the airlines direct as you cannot use the government ...

U4 ISSUE

U4 ISSUE

2.3 Overview of mitigating strategies ... U4 Issue 2012:8 Per diem policy analysis toolkit www.U4.no 2 The report is organized as follows.

10 Strategies to End Veteran Homelessness

10 Strategies to End Veteran Homelessness

10 Strategies to End Veteran ... accepting applicants regardless of their sobriety or use of substances, poor credit ... Grant and Per Diem Program ...