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

Solution:

We know that

The standard form is y = ax² + bx + c

Where a, b and c are real numbers

x and y are variables

The vertex form is y = a (x - 1)v + k

Where a, h and k are real numbers

x and y are variables

Given, the equation in vertex form is f(x) = 2(x - 1)² + 3.

We have to rewrite the equation in standard form.

The standard form of the equation is given by ax² + bx + c.

By using algebraic identity,

(a - b)² = a² - 2ab + b²

f(x) = 2(x² - 2x + 1) + 3

Using the distributive property

f(x) = 2x² - 4x + 2 + 3

So we get

f(x) = 2x² - 4x + 5

Therefore, the equation in standard form is f(x) = 2x² - 4x + 5.

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

Summary:

Rewriting f(x) = 2(x - 1)² + 3 from vertex form to standard form, the equation is f(x) = 2x² - 4x + 5.