What can you do to change the vertex form of a quadratic function to standard form?

Step-by-step explanation:

The vertex form of the quadratic equation is:  y = a(x - h)² + k.

The standard form of quadratic equation is: y = ax² + bx + c.

In order to change the vertex form into standard form, you'll have to expand the squared binomial, (x - h)² through FOIL method before distributing the value of a, and adding the value of k.

Example:

Given the vertex form, y = 2(x - 2)² + 2:

We can transform the given vertex form into its standard form as follows:

Step 1: expand (x - 2)² through FOIL method.

(x - 2)² = (x - 2)(x - 2) = x² - 2x - 2x + 4 =  x² - 4x + 4.

Step 2: Substitute the trinomial from step 1 into the equation.

y = 2(x - 2)² + 2

y = 2(x² - 4x + 4) + 2

Step 3: Distribute 2 into the parenthesis.

y = 2(x² - 4x + 4) + 2

y = 2x² - 8x + 8 + 2

Step 4: Combine like terms.

y = 2x² - 8x + 10  ⇒ This is the standard form of quadratic equation where a = 2, b = -8, and c = 10.  

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