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.