Math 2 (L1-3)
A.SSE.2, A.SSE.3, F.IF.8
Assessment Title: Factored Form Fever
Unit 3: Quadratic Functions: Working with Equations
Learning Targets:
 Factor a quadratic function given in standard form
 Interpret the factored form of a quadratic function to reveal its x-intercepts
We have used the zero product property to solve quadratic equations that are written in factored form. But often
times, quadratics functions are written in standard form. We are going to explore two different methods for
rewriting a quadratic in factored form. These are not the only ways to factor, but from these methods you may be
able to come up with more!
Recall: Standard Form => 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
Method 1: Area/Box Method
Given: 𝑓(𝑥 ) = 2𝑥 2 + 𝑥 − 6
1. Using a 2 x 2 box, write the first term in the upper left corner,
and the last term in the upper right corner
2𝑥 2
−6
2. Determine a combination of factors that multiply to produce a*c
and add to produce b.
**Note –the boxes along the diagonal should add to produce the
middle term of the quadratic**
𝐚𝐝𝐝 𝐭𝐨 𝐱
−3𝑥
4𝑥
−6
4 ∗ −3 = −12 𝑎𝑛𝑑 4 + −3 = 1
3. Determine the dimensions of each box and write them along the
left side and top.
4. Write the combinations of terms along the side and top of your
box as binomials
2𝑥 2
𝟐𝒙
−𝟑
𝒙
2𝑥 2
−3𝑥
𝟐
4𝑥
−6
(𝑥 + 2)(2𝑥 − 3)
Math 2 (L1-3)
A.SSE.2, A.SSE.3, F.IF.8
Assessment Title: Factored Form Fever
Unit 3: Quadratic Functions: Working with Equations
Method 1: Area/Box – You Try Two!
1) Given: 𝑓(𝑥) = 4𝑥 2 − 19𝑥 + 12
2) Given: 𝑓(𝑥) = 6𝑥 2 + 5𝑥 − 6
Math 2 (L1-3)
A.SSE.2, A.SSE.3, F.IF.8
Assessment Title: Factored Form Fever
Unit 3: Quadratic Functions: Working with Equations
Method 2: Diamond (X) Method
Given: 𝑓(𝑥 ) = 2𝑥 2 + 𝑥 − 6
1. Using the provided “diamond,” write a*c in the top of your diamond
and b in the bottom of your diamond
−12
1
2. Determine a combination of factors that multiply to produce a*c
and add to produce b
−12
−3
4
1
3. Rewrite your original quadratic replacing the middle term with the
two terms you found from your diamond
𝑓(𝑥) = 2𝑥 2 − 3𝑥 + 4𝑥 − 6
4. Rearrange your function to that you can group two terms together
with common factors (if needed)
𝑓(𝑥) = 2𝑥 2 + 4𝑥 − 3𝑥 − 6
5. Factor the greatest common factor from the first two terms and the
last two terms
𝑓(𝑥) = 2𝑥(𝑥 + 2) − 3(𝑥 + 2)
6. Factor the greatest common factor binomial from the function and
rewrite the leftover terms
𝑓(𝑥) = (𝑥 + 2)(2𝑥 − 3)
Method 2: Diamond (X) Method – You Try Two!
Math 2 (L1-3)
A.SSE.2, A.SSE.3, F.IF.8
Assessment Title: Factored Form Fever
Unit 3: Quadratic Functions: Working with Equations
1) 𝑓(𝑥) = 𝑥 2 − 13𝑥 + 40
2) 𝑓(𝑥) = 4𝑥 2 − 15𝑥 − 25
Math 2 (L1-3)
A.SSE.2, A.SSE.3, F.IF.8
Assessment Title: Factored Form Fever
Unit 3: Quadratic Functions: Working with Equations
Using one of the methods from above, find the key features of each quadratic function. If you have come up with
your own method for factoring, you may use it. You must show your work on each problem!
1.
2.
3.
4.
𝐺𝑖𝑣𝑒𝑛: 𝑓(𝑥) = 𝑥 2 − 10𝑥 + 24
a.
Determine the y-intercept? ( ______, ______)
b.
Rewrite this function in factored form: 𝑓(𝑥) = (
c.
What are the x-intercepts? ( ______, ______)
d.
Identify the vertex? ( ______, ______)
)(
)
( ______, ______)
𝐺𝑖𝑣𝑒𝑛: 𝑔(𝑥) = 𝑥 2 − 5𝑥 − 24
a.
Determine the y-intercept? ( ______, ______)
b.
Rewrite this function in factored form: 𝑓(𝑥) = (
c.
What are the x-intercepts? ( ______, ______)
d.
Identify the vertex? ( ______, ______)
)(
)
( ______, ______)
𝐺𝑖𝑣𝑒𝑛: ℎ(𝑥) = 20𝑥 − 𝑥 2
a.
Determine the y-intercept? ( ______, ______)
b.
Rewrite this function in factored form: 𝑓(𝑥) = (
c.
What are the x-intercepts? ( ______, ______)
d.
Identify the vertex? ( ______, ______)
)(
)
( ______, ______)
𝐺𝑖𝑣𝑒𝑛: 𝑏(𝑥) = 10𝑥 2 − 𝑥 − 21
a.
Determine the y-intercept? ( ______, ______)
b.
Rewrite this function in factored form: 𝑓(𝑥) = (
c.
What are the x-intercepts? ( ______, ______)
d.
Identify the vertex? ( ______, ______)
)(
( ______, ______)
)
Math 2 (L1-3)
A.SSE.2, A.SSE.3, F.IF.8
Assessment Title: Factored Form Fever
Unit 3: Quadratic Functions: Working with Equations
ANSWER KEY
We have used the zero product property to solve quadratic equations that are written in factored form. But often
times, quadratics functions are written in standard form. We are going to explore two different methods for
rewriting a quadratic in factored form. These are not the only ways to factor, but from these methods you may be
able to come up with more!
Recall: Standard Form => 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
Method 1: Area/Box Method
Given: 𝑓(𝑥 ) = 2𝑥 2 + 𝑥 − 6
1. Using a 2 x 2 box, write the first term in the upper left corner,
and the last term in the upper right corner
2𝑥 2
−6
2. Determine a combination of factors that multiply to produce a*c
and add to produce b.
**Note –the boxes along the diagonal should add to produce the
middle term of the quadratic**
𝐚𝐝𝐝 𝐭𝐨 𝐱
−3𝑥
4𝑥
−6
4 ∗ −3 = −12 𝑎𝑛𝑑 4 + −3 = 1
3. Determine the dimensions of each box and write them along the
left side and top.
4. Write the combinations of terms along the side and top of your
box as binomials
2𝑥 2
𝟐𝒙
−𝟑
𝒙
2𝑥 2
−3𝑥
𝟐
4𝑥
−6
(𝑥 + 2)(2𝑥 − 3)
Math 2 (L1-3)
A.SSE.2, A.SSE.3, F.IF.8
Assessment Title: Factored Form Fever
Unit 3: Quadratic Functions: Working with Equations
Method 1: Area/Box – You Try Two!
1) Given: 𝑓(𝑥) = 4𝑥 2 − 19𝑥 + 12
2) Given: 𝑓(𝑥) = 6𝑥 2 + 5𝑥 − 6
Math 2 (L1-3)
A.SSE.2, A.SSE.3, F.IF.8
Assessment Title: Factored Form Fever
Unit 3: Quadratic Functions: Working with Equations
Method 2: Diamond (X) Method
Given: 𝑓(𝑥 ) = 2𝑥 2 + 𝑥 − 6
1. Using the provided “diamond,” write a*c in the top of your diamond
and b in the bottom of your diamond
−12
1
2. Determine a combination of factors that multiply to produce a*c
and add to produce b
−12
−3
4
1
3. Rewrite your original quadratic replacing the middle term with the
two terms you found from your diamond
𝑓(𝑥) = 2𝑥 2 − 3𝑥 + 4𝑥 − 6
4. Rearrange your function to that you can group two terms together
with common factors (if needed)
𝑓(𝑥) = 2𝑥 2 + 4𝑥 − 3𝑥 − 6
5. Factor the greatest common factor from the first two terms and the
last two terms
𝑓(𝑥) = 2𝑥(𝑥 + 2) − 3(𝑥 + 2)
6. Factor the greatest common factor binomial from the function and
rewrite the leftover terms
𝑓(𝑥) = (𝑥 + 2)(2𝑥 − 3)
Method 2: Diamond (X) Method – You Try Two!
Math 2 (L1-3)
A.SSE.2, A.SSE.3, F.IF.8
Assessment Title: Factored Form Fever
Unit 3: Quadratic Functions: Working with Equations
1) 𝑓(𝑥) = 𝑥 2 − 13𝑥 + 40
2) 𝑓(𝑥) = 4𝑥 2 − 15𝑥 − 25
Math 2 (L1-3)
A.SSE.2, A.SSE.3, F.IF.8
Assessment Title: Factored Form Fever
Unit 3: Quadratic Functions: Working with Equations
Using one of the methods from above, find the key features of each quadratic function. If you have come up with
your own method for factoring, you may use it. You must show your work on each problem!
5.
6.
7.
8.
𝐺𝑖𝑣𝑒𝑛: 𝑓(𝑥) = 𝑥 2 − 10𝑥 + 24
e.
Determine the y-intercept? ( ______, ______)
f.
Rewrite this function in factored form: 𝑓(𝑥) = (
g.
What are the x-intercepts? ( ______, ______)
h.
Identify the vertex? ( ______, ______)
)(
)
( ______, ______)
𝐺𝑖𝑣𝑒𝑛: 𝑔(𝑥) = 𝑥 2 − 5𝑥 − 24
e.
Determine the y-intercept? ( ______, ______)
f.
Rewrite this function in factored form: 𝑓(𝑥) = (
g.
What are the x-intercepts? ( ______, ______)
h.
Identify the vertex? ( ______, ______)
)(
)
( ______, ______)
𝐺𝑖𝑣𝑒𝑛: ℎ(𝑥) = 20𝑥 − 𝑥 2
e.
Determine the y-intercept? ( ______, ______)
f.
Rewrite this function in factored form: 𝑓(𝑥) = (
g.
What are the x-intercepts? ( ______, ______)
h.
Identify the vertex? ( ______, ______)
)(
)
( ______, ______)
𝐺𝑖𝑣𝑒𝑛: 𝑏(𝑥) = 10𝑥 2 − 𝑥 − 21
e.
Determine the y-intercept? ( ______, ______)
f.
Rewrite this function in factored form: 𝑓(𝑥) = (
g.
What are the x-intercepts? ( ______, ______)
h.
Identify the vertex? ( ______, ______)
)(
( ______, ______)
)