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Translating vertex form into standard form when a is not equal to 1

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ChristianManzo5

The document provides steps for translating a quadratic function from vertex form to standard form when a 1. It explains that the vertex form can be written as the square of a binomial. Using FOIL multiplication and the distributive property, the terms can be distributed and combined to obtain the standard form. Two examples are provided and worked through to demonstrate the process.

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Translating Quadratic Function from Vertex Form into Standard Form if Mathematics 9
Standard From and Vertex Form of Quadratic Function Vertex Form = 2 + Standard Form = 2 + +
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
Vertex Form into Standard Form Steps for translating quadratic function from vertex back to standard form if Step 1: Since the vertex form of quadratic equation is written in the form of = 2 + , and we have a square of binomial which is 2, then we can replace it by ( )( ). See the example below. Example 1: = 2 3 2 + 6 = 2 3 3 + 6
Vertex Form into Standard Form Steps for translating quadratic function from vertex back to standard form if 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: = 2( 3)( 3) + 6 F = = O = = I = = L = = = 2(2 3 3 + 9) + 6 Do not forget to put parenthesis because the product of the two binomials are still multiplied by 2.
Vertex Form into Standard Form Steps for translating quadratic function from vertex back to standard form if Step 3: Simplify the terms inside the parenthesis by combining like terms Example 1: = 2(2 3 3 + 9) + 6 6 = 2(2 6 + 9) + 6
Vertex Form into Standard Form Steps for translating quadratic function from vertex back to standard form if Step 4: By distributive Property, distribute 2 to all terms inside the parenthesis. Example 1: = 2(2 6 + 9) + 6 = 22 12 + 18 + 6 2 2 = 22 2 6 = 12 2 9 = 18
Vertex Form into Standard Form Steps for translating quadratic function from vertex back to standard form if Step 5: The last step is to combine the two constant terms. Example 1: = 22 12 + 18 + 6 24 = 22 12 + 24 Final Answer This is already the standard form of the equation = 2 3 2 + 6
More Examples Translating Vertex into Standard Form when 1
Example 1 = + Quadratic in Vertex Form = + Square of binomial + 2 = ( + ( + ) = + + FOIL Method = ( + ) + Simplify the result of FOIL = + + Distributive Property = + Combine like terms = + Final Answer Find the standard form of the function = + .
Example 2 = + Quadratic in Vertex Form = + + Square of binomial + 2 = ( + ( + ) = + + + FOIL Method = ( + + ) Simplify the result of FOIL = + + Distributive Property = + + Combine like terms = + + Final Answer Find the standard form of the function = + .

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Translating vertex form into standard form when a is not equal to 1

  • 1. Translating Quadratic Function from Vertex Form into Standard Form if Mathematics 9
  • 2. Standard From and Vertex Form of Quadratic Function Vertex Form = 2 + Standard Form = 2 + +
  • 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 Step 1: Since the vertex form of quadratic equation is written in the form of = 2 + , and we have a square of binomial which is 2, then we can replace it by ( )( ). See the example below. Example 1: = 2 3 2 + 6 = 2 3 3 + 6
  • 5. Vertex Form into Standard Form Steps for translating quadratic function from vertex back to standard form if 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: = 2( 3)( 3) + 6 F = = O = = I = = L = = = 2(2 3 3 + 9) + 6 Do not forget to put parenthesis because the product of the two binomials are still multiplied by 2.
  • 6. Vertex Form into Standard Form Steps for translating quadratic function from vertex back to standard form if Step 3: Simplify the terms inside the parenthesis by combining like terms Example 1: = 2(2 3 3 + 9) + 6 6 = 2(2 6 + 9) + 6
  • 7. Vertex Form into Standard Form Steps for translating quadratic function from vertex back to standard form if Step 4: By distributive Property, distribute 2 to all terms inside the parenthesis. Example 1: = 2(2 6 + 9) + 6 = 22 12 + 18 + 6 2 2 = 22 2 6 = 12 2 9 = 18
  • 8. Vertex Form into Standard Form Steps for translating quadratic function from vertex back to standard form if Step 5: The last step is to combine the two constant terms. Example 1: = 22 12 + 18 + 6 24 = 22 12 + 24 Final Answer This is already the standard form of the equation = 2 3 2 + 6
  • 9. More Examples Translating Vertex into Standard Form when 1
  • 10. Example 1 = + Quadratic in Vertex Form = + Square of binomial + 2 = ( + ( + ) = + + FOIL Method = ( + ) + Simplify the result of FOIL = + + Distributive Property = + Combine like terms = + Final Answer Find the standard form of the function = + .
  • 11. Example 2 = + Quadratic in Vertex Form = + + Square of binomial + 2 = ( + ( + ) = + + + FOIL Method = ( + + ) Simplify the result of FOIL = + + Distributive Property = + + Combine like terms = + + Final Answer Find the standard form of the function = + .