Convert Vertex Form to Standard Form: Explore (x-2)² + 4

Find the standard representation of the following function

$f(x)=(x-2)^2+4$

We need to convert the given function $f(x) = (x-2)^2 + 4$ to standard form.

To expand $(x-2)^2$, we use the formula $(a-b)^2 = a^2 - 2ab + b^2$. Applying this to $(x-2)^2$, we get:

• $(x-2)^2 = x^2 - 4x + 4$.

This accounts for the expanded square. Next, we add the constant term $4$ from the original function $(x-2)^2 + 4$:

• $f(x) = x^2 - 4x + 4 + 4$.

Simplify by combining the constant terms:

• $f(x) = x^2 - 4x + 8$.

The standard form of the function is thus $f(x) = x^2 - 4x + 8$.