The document explains how to convert a quadratic function from vertex form to standard form when a = 1, using the vertex form equation y = a(x − h)² + k. It provides a step-by-step method that involves replacing the square of the binomial, using the FOIL method for multiplication, and combining like terms. Multiple examples illustrate the process of simplifying the equation to achieve the standard form y = ax² + bx + c.

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.