Skill 3: Converting Quadratic Functions from Standard to Vertex Form
VERTEX FORM
STANDARD FORM
Standard Form
Factored
Form
The goal of today’s lesson is to go from STANDARD FORM to FACTORED FORM
with a bit of detail to pay attention.
Creating a Perfect Square Trinomial
Use completing the square to find the value of c that makes
You can form a perfect square trinomial from
by adding
.
Example #1: What term would you have to add to the expression to make it a perfect square trinomial?
a)
b) 2
What if
?
⇾
FACTOR OUT ‘a’ VALUE!
c)
Converting from Standard Form into Vertex Form by Completing the Square
Example #2: Convert the function from standard form into vertex form by completing the square. Then, identify
the vertex.
1. Isolate the last number.
2. If a is not 1, then pull it out!
3. Add and subtract
inside
of the parenthesis.
4. Factor three trinomial.
5. Factor out the last number
we didn’t use.
6. Add the last two numbers.
Example #4: Convert the function from standard form into vertex form by completing the square. Then, identify
the vertex.
1. Isolate the last number.
2. If a is not 1, then pull it out!
3. Add and subtract
inside
of the parenthesis.
4. Factor three trinomial.
5. Factor out the last number
we didn’t use.
6. Add the last two numbers.
Example #5: Convert the function from standard form into vertex form by completing the square. Then, identify
the vertex.
Example #6: Convert the function from standard form into vertex form by completing the square. Then, identify
the vertex.
Example #7: Convert the function from standard form into vertex form by completing the square. Then, identify
the vertex.