Rewrite f(x) = 3(x - 2)² + 1 from vertex form to standard form.

Solution:

The given equation :

f(x) = 3(x - 2)² + 1 is in vertex form

i.e., f(x) = a(x - h)² + k, with (h, k) as vertex.

Here we have a vertex as (2, 1).

Standard form of the equation is:

f(x) = ax² + bx + c.

f(x) = 3(x - 2)² + 1

Using the algebraic identity

(a - b)² = a² + b² - 2ab

f(x) = 3(x² - 4x +4) + 1.

Using the distributive property

f(x) = 3[x² - 4x + 4] + 1

f(x) = 3x² - 12x + 12 + 1

f(x) = 3x² - 12x + 13

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Rewrite f(x) = 3(x - 2)² + 1 from vertex form to standard form.

Summary:

Rewriting f(x) = 3(x - 2)² + 1 from vertex form to standard form we get, f(x) = 3x² - 12x + 13.