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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.
2. Standard From and Vertex Form of
Quadratic Function
๏ดVertex Form
๐ฆ = ๐ ๐ฅ โ โ 2
+ ๐
๏ดStandard Form
๐ฆ = ๐๐ฅ2
+ ๐๐ฅ + ๐
3. ๏ดTo 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
๏ด Steps for translating quadratic function from vertex back
to standard form if ๐ = ๐
Step 1: Since the vertex form of quadratic equation is written in the
form of ๐ฆ = ๐ ๐ฅ โ โ 2 + ๐, and we have a square of binomial
which is ๐ฅ โ โ 2, then we can replace it by (๐ฅ โ โ)(๐ฅ โ โ). See
the example below.
Example 1:
๐ฆ = ๐ฅ + 2 2
+ 3
๐ฆ = (๐ฅ + 2)(๐ฅ + 2) + 3
v
5. Vertex Form into Standard Form
๏ด Steps for translating quadratic function from vertex back
to standard form if ๐ = ๐
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:
๐ฆ = (๐ฅ + 2)(๐ฅ + 2) + 3
๐ญ
๐ถ
๐ฐ
๐ณ
F = ๐ ๐ = ๐ ๐
O = ๐ ๐ = ๐๐
I = ๐ ๐ = ๐๐
L = ๐ ๐ = ๐
๐ฆ = ๐ฅ2 + 2๐ฅ + 2๐ฅ + 4 + 3
6. Vertex Form into Standard Form
๏ด Steps for translating quadratic function from vertex back
to standard form if ๐ = ๐
Step 3: Then, the last step is to combine like terms and were done ๏
๐ฆ = ๐ฅ2
+ 2๐ฅ + 2๐ฅ + 4 + 3
4๐ฅ 7
๐ฆ = ๐ฅ2 + 4๐ฅ + 7
This is already the
standard form of
the equation
๐ฆ = ๐ฅ + 2 2 + 3
Final Answer