Transforming the Function: Reveal the Standard Form of f(x) = (x+5)² + 3

Find the standard representation of the following function

$f(x)=(x+5)^2+3$

To convert the given quadratic function into its standard form, follow these steps:

• Step 1: Expand the Binomial
  We begin with the function in vertex form: $f(x) = (x + 5)^2 + 3$. The expression $(x + 5)^2$ can be expanded using the binomial theorem: $(a + b)^2 = a^2 + 2ab + b^2$.

• Step 2: Apply the Expansion Formula
  Let $a = x$ and $b = 5$. Therefore, $(x + 5)^2 = x^2 + 2 \times x \times 5 + 5^2 = x^2 + 10x + 25$.

• Step 3: Add the Constant
  Now, add the constant 3 to this expanded result: $x^2 + 10x + 25 + 3 = x^2 + 10x + 28$.

Thus, the standard representation of the function is $f(x) = x^2 + 10x + 28$.

Given the choices, the correct answer is $f(x) = x^2 + 10x + 28$, which matches choice 2.