Algebra 1 week 8 learn it 1

1. Example 1: Solve the quadratic equation 2𝑥2 − 7𝑥 − 15 = 0
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

2. Example 1: Solve the quadratic equation 2𝑥2 − 7𝑥 − 15 = 0
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

3. Example 1: Solve the quadratic equation 2𝑥2 − 7𝑥 − 15 = 0
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

4. Example 1: Solve the quadratic equation 2𝑥2 − 7𝑥 − 15 = 0
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

5. Example 1: Solve the quadratic equation 2𝑥2 − 7𝑥 − 15 = 0
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

6. Example 1: Solve the quadratic equation 2𝑥2 − 7𝑥 − 15 = 0
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

7. Example 1: Solve the quadratic equation 2𝑥2 − 7𝑥 − 15 = 0
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

8. Example 1: Solve the quadratic equation 2𝑥2 − 7𝑥 − 15 = 0
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

9. Example 1: Solve the quadratic equation 2𝑥2 − 7𝑥 − 15 = 0
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

10. Example 1: Solve the quadratic equation 2𝑥2 − 7𝑥 − 15 = 0
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

11. Example 1: Solve the quadratic equation 2𝑥2 − 7𝑥 − 15 = 0
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

12. Example 1: Solve the quadratic equation 2𝑥2 − 7𝑥 − 15 = 0
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

13. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

14. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

15. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

16. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

17. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

18. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

19. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

20. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

21. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

22. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

23. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

24. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

25. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

26. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x

27. Example 2: Solve the quadratic equation 4𝑥2 − 8𝑥 = 5
Steps Work
1. Write a, b, and c from the equation
2. Find two integers that…
• Multiply to a×c
AND
• Add to b
3. Rewrite the equation – split b using the
integers from Step 2
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x