Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x...
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Transcript of Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x...
![Page 1: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/1.jpg)
Holt Algebra 1
9-6 Solving Quadratic Equations by Factoring
Warm UpFind each product.
1. (x + 2)(x + 7) 2. (x – 11)(x + 5)
3. (x – 10)2
Factor each polynomial.
4. x2 + 12x + 35 5. x2 + 2x – 63
6. x2 – 10x + 16 7. 2x2 – 16x + 32
x2 + 9x + 14 x2 – 6x – 55 x2 – 20x + 100
(x + 5)(x + 7) (x – 7)(x + 9)
(x – 2)(x – 8) 2(x – 4)2
![Page 2: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/2.jpg)
Holt Algebra 1
9-6 Solving Quadratic Equations by Factoring
9-6 Solving Quadratic Equations by Factoring
Holt Algebra 1
![Page 3: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/3.jpg)
Holt Algebra 1
9-6 Solving Quadratic Equations by Factoring
![Page 4: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/4.jpg)
Holt Algebra 1
9-6 Solving 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
x – 7 = 0 or x + 2 = 0
x = 7 or x = –2
The solutions are 7 and –2.
Use the Zero Product Property.
Solve each equation.
![Page 5: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/5.jpg)
Holt Algebra 1
9-6 Solving Quadratic Equations by Factoring
Example 1A Continued
Use the Zero Product Property to solve the equation. Check your answer.
Substitute each solution for x into the original equation.
Check (x – 7)(x + 2) = 0
(7 – 7)(7 + 2) 0(0)(9) 0
0 0Check (x – 7)(x + 2) = 0
(–2 – 7)(–2 + 2) 0(–9)(0) 0
0 0
![Page 6: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/6.jpg)
Holt Algebra 1
9-6 Solving 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
x = 0 or x – 2 = 0x = 2
The solutions are 0 and 2.
Use the Zero Product Property.
Solve the second equation.
Substitute each solution for x into
the original equation.
Check (x – 2)(x) = 0
(0 – 2)(0) 0
(–2)(0) 00 0
(x – 2)(x) = 0
(2 – 2)(2) 0 (0)(2) 0
0 0
(x)(x – 2) = 0
![Page 7: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/7.jpg)
Holt Algebra 1
9-6 Solving Quadratic Equations by Factoring
Example 2A: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
x2 – 6x + 8 = 0
(x – 4)(x – 2) = 0
x – 4 = 0 or x – 2 = 0
x = 4 or x = 2The solutions are 4 and 2.
Factor the trinomial.
Use the Zero Product Property.
Solve each equation.
x2 – 6x + 8 = 0
(4)2 – 6(4) + 8 016 – 24 + 8 0
0 0
Checkx2 – 6x + 8 = 0
(2)2 – 6(2) + 8 0 4 – 12 + 8 0
0 0
Check
![Page 8: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/8.jpg)
Holt Algebra 1
9-6 Solving Quadratic Equations by Factoring
Example 2B: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
x2 + 4x = 21x2 + 4x = 21
–21 –21x2 + 4x – 21 = 0
(x + 7)(x –3) = 0
x + 7 = 0 or x – 3 = 0
x = –7 or x = 3
The solutions are –7 and 3.
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 9: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/9.jpg)
Holt Algebra 1
9-6 Solving Quadratic Equations by Factoring
Example 2D: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
–2x2 = 20x + 50
The equation must be written in standard form. So add 2x2 to both sides.
Factor out the GCF 2.
+2x2 +2x2
0 = 2x2 + 20x + 50
–2x2 = 20x + 50
2x2 + 20x + 50 = 0
2(x2 + 10x + 25) = 0
Factor the trinomial.2(x + 5)(x + 5) = 0
2 ≠ 0 or x + 5 = 0
x = –5
Use the Zero Product Property.
Solve the equation.
![Page 10: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/10.jpg)
Holt Algebra 1
9-6 Solving Quadratic Equations by Factoring
Check It Out! Example 2c
Solve the quadratic equation by factoring. Check your answer.
30x = –9x2 – 25
–9x2 – 30x – 25 = 0
–1(3x + 5)(3x + 5) = 0
–1(9x2 + 30x + 25) = 0
–1 ≠ 0 or 3x + 5 = 0
Write the equation in standard form.
Factor the trinomial.
Use the Zero Product Property. – 1 cannot equal 0.
Solve the remaining equation.
Factor out the GCF, –1.
![Page 11: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/11.jpg)
Holt Algebra 1
9-6 Solving Quadratic Equations by Factoring
Check It Out! Example 3
What if…? The equation for the height above the water for another diver can be modeled by h = –16t2 + 8t + 24. Find the time it takes this diver to reach the water.
h = –16t2 + 8t + 24
0 = –16t2 + 8t + 24
0 = –8(2t2 – t – 3)
0 = –8(2t – 3)(t + 1)
The diver reaches the water when h = 0.
Factor out the GFC, –8.
Factor the trinomial.
![Page 12: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/12.jpg)
Holt Algebra 1
9-6 Solving Quadratic Equations by Factoring
–8 ≠ 0, 2t – 3 = 0 or t + 1= 0 Use the Zero Product Property.
2t = 3 or t = –1 Solve each equation.
Since time cannot be negative, –1 does not make sense in this situation.
It takes the diver 1.5 seconds to reach the water.
Check 0 = –16t2 + 8t + 24
Substitute 1 into the original equation.
0 –16(1.5)2 + 8(1.5) + 24
0 –36 + 12 + 24 0 0
Check It Out! Example 3 Continued
t = 1.5
![Page 13: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/13.jpg)
Holt Algebra 1
9-6 Solving Quadratic Equations by Factoring
![Page 14: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/14.jpg)
Holt Algebra 1
9-6 Solving Quadratic Equations by Factoring
Lesson Quiz: Part I
Use the Zero Product Property to solve each equation. Check your answers.
1. (x – 10)(x + 5) = 0
2. (x + 5)(x) = 0
Solve each quadratic equation by factoring. Check your answer.
3. x2 + 16x + 48 = 0
4. x2 – 11x = –24 •
10, –5
–5, 0
–4, –12
3, 8
![Page 15: Holt Algebra 1 9-6 Solving Quadratic Equations by Factoring Warm Up Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial.](https://reader035.fdocuments.net/reader035/viewer/2022082204/5697c0271a28abf838cd6678/html5/thumbnails/15.jpg)
Holt Algebra 1
9-6 Solving Quadratic Equations by Factoring
Lesson Quiz: Part II
1, –7
–9
–2
5 s
5. 2x2 + 12x – 14 = 0
6. x2 + 18x + 81 = 0
7. –4x2 = 16x + 16
8. The height of a rocket launched upward from a 160 foot cliff is modeled by the function h(t) = –16t2 + 48t + 160, where h is height in feet and t is time in seconds. Find the time it takes the rocket to reach the ground at the bottom of the cliff.