1. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
2. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
3. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
4. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
5. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
Tip: Use the Integer
Multiplication Chart
6. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
Tip: Use the Integer
Multiplication Chart
7. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
8. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
9. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
10. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
11. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
12. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
13. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
14. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…then find its factors!
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
15. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…then find its factors!
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
16. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…then find its factors!
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
17. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…then find its factors!
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
18. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…then find its factors!
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
Note: the factors make the
factored form of the
function
19. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…then find its factors!
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
20. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…then find its factors!
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
21. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…then find its factors!
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
22. Example 1: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 + 6𝑥 + 8
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…then find its factors!
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
23. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
24. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
25. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
28. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
29. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
30. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
31. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
32. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
33. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
34. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
35. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
36. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
37. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
38. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts
39. Example 2: Find the x-intercepts of the quadratic function 𝑓 𝑥 = 𝑥2 − 7𝑥 + 12
Steps Work
1. Replace 𝒇 𝒙 with 0
2. Write a, b, and c from the equation
3. Find two integers that…
• Multiply to a×c
AND
• Add to b
4. Rewrite the function – split b using
the integers from Step 3
5. Make a “reverse” Multiplication
Frame…and “undo” it
6. Let each factor = 0
7. Solve for x
8. Write the x-intercepts