Hello! This presentation contains step by step process on how to translate quadratic function from vertex form back to standard form when the value of a is equal to 1.

1. Translating Quadratic
Function from Vertex Form
into Standard Form if 𝒂 = 𝟏
Mathematics 9

2. Standard From and Vertex Form of
Quadratic Function
Vertex Form
𝑦 = 𝑎 𝑥 − ℎ 2
+ 𝑘
Standard Form
𝑦 = 𝑎𝑥2
+ 𝑏𝑥 + 𝑐

3. To translate quadratic
function from vertex form back
to standard form, all we need
to do is to simplify and you
should know the following:
1. FOIL Method
2. Distributive Property

4. Vertex Form into Standard Form
 Steps for translating quadratic function from vertex back
to standard form if 𝒂 = 𝟏
Step 1: Since the vertex form of quadratic equation is written in the
form of 𝑦 = 𝑎 𝑥 − ℎ 2 + 𝑘, and we have a square of binomial
which is 𝑥 − ℎ 2, then we can replace it by (𝑥 − ℎ)(𝑥 − ℎ). See
the example below.
Example 1:
𝑦 = 𝑥 + 2 2
+ 3
𝑦 = (𝑥 + 2)(𝑥 + 2) + 3
v

5. Vertex Form into Standard Form
 Steps for translating quadratic function from vertex back
to standard form if 𝒂 = 𝟏
Step 2: Now, we have two binomials and the operation is
multiplication, and to get the product of two binomials, we need to
use the FOIL method.
Example 1:
𝑦 = (𝑥 + 2)(𝑥 + 2) + 3
𝑭
𝑶
𝑰
𝑳
F = 𝒙 𝒙 = 𝒙 𝟐
O = 𝒙 𝟐 = 𝟐𝒙
I = 𝟐 𝒙 = 𝟐𝒙
L = 𝟐 𝟐 = 𝟒
𝑦 = 𝑥2 + 2𝑥 + 2𝑥 + 4 + 3

6. Vertex Form into Standard Form
 Steps for translating quadratic function from vertex back
to standard form if 𝒂 = 𝟏
Step 3: Then, the last step is to combine like terms and were done 
𝑦 = 𝑥2
+ 2𝑥 + 2𝑥 + 4 + 3
4𝑥 7
𝑦 = 𝑥2 + 4𝑥 + 7
This is already the
standard form of
the equation
𝑦 = 𝑥 + 2 2 + 3
Final Answer

7. More Examples
Translating Vertex into Standard Form when 𝑎 = 1

8. Example 1
𝒚 = 𝒙 + 𝟑 𝟐 + 𝟏 Quadratic in Vertex Form
𝒚 = 𝒙 + 𝟑 𝒙 + 𝟑 + 𝟏
Square of binomial
𝑎 + 𝑏 2
= (𝑎 + 𝑏(𝑎 + 𝑏)
𝒚 = (𝒙 𝟐
+ 𝟑𝒙 + 𝟑𝒙 + 𝟗) + 𝟏 FOIL Method
𝒚 = 𝒙 𝟐 + 𝟔𝒙 + 𝟗 + 𝟏 Simplify and remove parenthesis
𝒚 = 𝒙 𝟐
+ 𝟔𝒙 + 𝟏𝟎 Combine like terms
𝒚 = 𝒙 𝟐
+ 𝟔𝒙 + 𝟏𝟎 Final Answer
Find the standard form of the function 𝒚 = 𝒙 + 𝟑 𝟐
+ 𝟏.

9. Example 1
𝒚 = 𝒙 +
𝟏
𝟐
𝟐
− 𝟒 Quadratic in Vertex Form
𝒚 = 𝒙 +
𝟏
𝟐
𝒙 +
𝟏
𝟐
− 𝟒
Square of binomial
𝑎 + 𝑏 2 = (𝑎 + 𝑏(𝑎 + 𝑏)
𝒚 = 𝒙 𝟐
+
𝟏
𝟐
𝒙 +
𝟏
𝟐
𝒙 +
𝟏
𝟒
− 𝟒 FOIL Method
𝒚 = 𝒙 𝟐 + 𝒙 +
𝟏
𝟒
− 𝟒 Simplify and remove parenthesis
𝒚 = 𝒙 𝟐
+ 𝒙 −
𝟏𝟓
𝟒
Combine like terms
𝒚 = 𝒙 𝟐 + 𝒙 −
𝟏𝟓
𝟒
Final Answer
Find the standard form of the function 𝒚 = 𝒙 +
𝟏
𝟐
𝟐
− 𝟒.