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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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
10 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100
9 -90 -81 -72 -63 -54 -45 -36 -27 -18 -9 0 9 18 27 36 45 54 63 72 81 90
8 -80 -72 -64 -56 -48 -40 -32 -24 -16 -8 0 8 16 24 32 40 48 56 64 72 80
7 -70 -63 -56 -49 -42 -35 -28 -21 -14 -7 0 7 14 21 28 35 42 49 56 63 70
6 -60 -54 -48 -42 -36 -30 -24 -18 -12 -6 0 6 12 18 24 30 36 42 48 54 60
5 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50
4 -40 -36 -32 -28 -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24 28 32 36 40
3 -30 -27 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 21 24 27 30
2 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20
1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
-2 20 18 16 14 12 10 8 6 4 2 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20
-3 30 27 24 21 18 15 12 9 6 3 0 -3 -6 -9 -12 -15 -18 -21 -24 -27 -30
-4 40 36 32 28 24 20 16 12 8 4 0 -4 -8 -12 -16 -20 -24 -28 -32 -36 -40
-5 50 45 40 35 30 25 20 15 10 5 0 -5 -10 -15 -20 -25 -30 -35 -40 -45 -50
-6 60 54 48 42 36 30 24 18 12 6 0 -6 -12 -18 -24 -30 -36 -42 -48 -54 -60
-7 70 63 56 49 42 35 28 21 14 7 0 -7 -14 -21 -28 -35 -42 -49 -56 -63 -70
-8 80 72 64 56 48 40 32 24 16 8 0 -8 -16 -24 -32 -40 -48 -56 -64 -72 -80
-9 90 81 72 63 54 45 36 27 18 9 0 -9 -18 -27 -36 -45 -54 -63 -72 -81 -90
Tip: Use the Integer
Multiplication Chart
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
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
10 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100
9 -90 -81 -72 -63 -54 -45 -36 -27 -18 -9 0 9 18 27 36 45 54 63 72 81 90
8 -80 -72 -64 -56 -48 -40 -32 -24 -16 -8 0 8 16 24 32 40 48 56 64 72 80
7 -70 -63 -56 -49 -42 -35 -28 -21 -14 -7 0 7 14 21 28 35 42 49 56 63 70
6 -60 -54 -48 -42 -36 -30 -24 -18 -12 -6 0 6 12 18 24 30 36 42 48 54 60
5 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50
4 -40 -36 -32 -28 -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24 28 32 36 40
3 -30 -27 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 21 24 27 30
2 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20
1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
-2 20 18 16 14 12 10 8 6 4 2 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20
-3 30 27 24 21 18 15 12 9 6 3 0 -3 -6 -9 -12 -15 -18 -21 -24 -27 -30
-4 40 36 32 28 24 20 16 12 8 4 0 -4 -8 -12 -16 -20 -24 -28 -32 -36 -40
-5 50 45 40 35 30 25 20 15 10 5 0 -5 -10 -15 -20 -25 -30 -35 -40 -45 -50
-6 60 54 48 42 36 30 24 18 12 6 0 -6 -12 -18 -24 -30 -36 -42 -48 -54 -60
-7 70 63 56 49 42 35 28 21 14 7 0 -7 -14 -21 -28 -35 -42 -49 -56 -63 -70
-8 80 72 64 56 48 40 32 24 16 8 0 -8 -16 -24 -32 -40 -48 -56 -64 -72 -80
-9 90 81 72 63 54 45 36 27 18 9 0 -9 -18 -27 -36 -45 -54 -63 -72 -81 -90
Tip: Use the Integer
Multiplication Chart
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
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
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
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
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
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
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
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
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
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
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
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

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Algebra 1 week 6 learn it 1

  • 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
  • 26. 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 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 9 -90 -81 -72 -63 -54 -45 -36 -27 -18 -9 0 9 18 27 36 45 54 63 72 81 90 8 -80 -72 -64 -56 -48 -40 -32 -24 -16 -8 0 8 16 24 32 40 48 56 64 72 80 7 -70 -63 -56 -49 -42 -35 -28 -21 -14 -7 0 7 14 21 28 35 42 49 56 63 70 6 -60 -54 -48 -42 -36 -30 -24 -18 -12 -6 0 6 12 18 24 30 36 42 48 54 60 5 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 4 -40 -36 -32 -28 -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24 28 32 36 40 3 -30 -27 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 21 24 27 30 2 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -2 20 18 16 14 12 10 8 6 4 2 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -3 30 27 24 21 18 15 12 9 6 3 0 -3 -6 -9 -12 -15 -18 -21 -24 -27 -30 -4 40 36 32 28 24 20 16 12 8 4 0 -4 -8 -12 -16 -20 -24 -28 -32 -36 -40 -5 50 45 40 35 30 25 20 15 10 5 0 -5 -10 -15 -20 -25 -30 -35 -40 -45 -50 -6 60 54 48 42 36 30 24 18 12 6 0 -6 -12 -18 -24 -30 -36 -42 -48 -54 -60 -7 70 63 56 49 42 35 28 21 14 7 0 -7 -14 -21 -28 -35 -42 -49 -56 -63 -70 -8 80 72 64 56 48 40 32 24 16 8 0 -8 -16 -24 -32 -40 -48 -56 -64 -72 -80 -9 90 81 72 63 54 45 36 27 18 9 0 -9 -18 -27 -36 -45 -54 -63 -72 -81 -90 Tip: Use the Integer Multiplication Chart
  • 27. 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 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 9 -90 -81 -72 -63 -54 -45 -36 -27 -18 -9 0 9 18 27 36 45 54 63 72 81 90 8 -80 -72 -64 -56 -48 -40 -32 -24 -16 -8 0 8 16 24 32 40 48 56 64 72 80 7 -70 -63 -56 -49 -42 -35 -28 -21 -14 -7 0 7 14 21 28 35 42 49 56 63 70 6 -60 -54 -48 -42 -36 -30 -24 -18 -12 -6 0 6 12 18 24 30 36 42 48 54 60 5 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 4 -40 -36 -32 -28 -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24 28 32 36 40 3 -30 -27 -24 -21 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 21 24 27 30 2 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -2 20 18 16 14 12 10 8 6 4 2 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -3 30 27 24 21 18 15 12 9 6 3 0 -3 -6 -9 -12 -15 -18 -21 -24 -27 -30 -4 40 36 32 28 24 20 16 12 8 4 0 -4 -8 -12 -16 -20 -24 -28 -32 -36 -40 -5 50 45 40 35 30 25 20 15 10 5 0 -5 -10 -15 -20 -25 -30 -35 -40 -45 -50 -6 60 54 48 42 36 30 24 18 12 6 0 -6 -12 -18 -24 -30 -36 -42 -48 -54 -60 -7 70 63 56 49 42 35 28 21 14 7 0 -7 -14 -21 -28 -35 -42 -49 -56 -63 -70 -8 80 72 64 56 48 40 32 24 16 8 0 -8 -16 -24 -32 -40 -48 -56 -64 -72 -80 -9 90 81 72 63 54 45 36 27 18 9 0 -9 -18 -27 -36 -45 -54 -63 -72 -81 -90 Tip: Use the Integer Multiplication Chart
  • 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