9-6 solving quadratic equations 9-6by...
TRANSCRIPT
![Page 1: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/1.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring9-6Solving Quadratic Equations by Factoring
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
![Page 2: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/2.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Bell Quiz 9-6Find each product.
1. (x + 2)(x + 7) 2. (x – 11)(x + 5)
Factor each polynomial.
3. x2 + 12x + 35 4. x2 + 2x – 63
5. x2 – 10x + 16 10 pts possible
2 pts 2 pts
2 pts2 pts
2 pts
![Page 3: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/3.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Questions on 9-1
![Page 4: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/4.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Solve quadratic equations by factoring.
Objective
![Page 5: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/5.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
A method used to solve quadratic equations is to factor and use the Zero Product Property.
![Page 6: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/6.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Example 1A: Use the Zero Product Property
Use the Zero Product Property to solve the equation. Check your answer.
(x – 7)(x + 2) = 0
Use the Zero Product
Property.
Solve each equation.
Substitute each
solution for x into the
original equation.
![Page 7: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/7.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Example 1B: Use the Zero Product Property
Use the Zero Product Property to solve each equation. Check your answer.
(x – 2)(x) = 0
Use the Zero Product
Property.
Solve the second
equation.
Substitute each
solution for x into the
original equation.
![Page 8: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/8.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Use the Zero Product Property to solve each equation. Check your answer.
Check It Out! Example 1
1a: (x)(x + 4) = 0 1b: (x + 4)(x – 3) = 0
![Page 9: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/9.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
If a quadratic equation is written in standard form, ax2 + bx + c = 0, then to solve the equation, you may need to factor before using the Zero Product Property.
![Page 10: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/10.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
To review factoring techniques, see lessons 8-3 through 8-5.
Helpful Hint
![Page 11: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/11.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Example 2A: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
x2 – 6x + 8 = 0
Factor the trinomial.
Use the Zero Product
Property. Solve each equation.
![Page 12: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/12.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Example 2B: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
x2 + 4x = 21 The equation must be
written in standard
form. So subtract
21 from both sides.
Factor the trinomial.
Use the Zero
Product Property.
Solve each equation.
![Page 13: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/13.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Example 2C: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
x2 – 12x + 36 = 0
Factor the trinomial.
Use the Zero
Product Property.
Solve each equation.
![Page 14: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/14.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
Example 2D: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
–2x2 = 20x + 50The equation must be
written in standard
form. So add 2x2 to
both sides.
Factor out the GCF 2.
Factor the trinomial.
Use the Zero Product
Property.
Solve the equation.
![Page 15: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/15.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
(x – 3)(x – 3) is a perfect square. Since both factors are the same, you solve only one of them.
Helpful Hint
![Page 16: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/16.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by FactoringCheck It Out! Example 2
Solve the quadratic equation by factoring. Check your answer.
2a: x2 – 6x + 9 = 0 2b: x2 + 4x = 5
![Page 17: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/17.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by FactoringCheck It Out! Example 2
Solve the quadratic equation by factoring. Check your answer.
2c: 30x = –9x2 – 25 2d: 3x2 – 4x + 1 = 0
![Page 18: 9-6 Solving Quadratic Equations 9-6by Factoringblog.wsd.net/rejohnson/files/2011/04/6th-A1CH9L6.pdf · · 2011-04-27Holt Algebra 1 9-6Solving Quadratic Equations by Factoring Bell](https://reader030.vdocuments.mx/reader030/viewer/2022021507/5b0453da7f8b9a8c688d7440/html5/thumbnails/18.jpg)
Holt Algebra 1
9-6Solving Quadratic Equations
by Factoring
�Section 9-6 (page 633) 1-6, 9, 11, 15, 18, 20, 21, 23, 25, 26, 28, 29, 41, 44, 49, 61, 62, 65