Find the Standard Form of the Function: Transforming (x+4)² - 16

Find the standard representation of the following function

$f(x)=(x+4)^2-16$

To solve this problem, we'll follow these steps:

• Step 1: Expand $(x + 4)^2$ using the formula $(a + b)^2 = a^2 + 2ab + b^2$.
• Step 2: Simplify the expression by subtracting 16 from the expanded result.
• Step 3: Write the simplified expression in the standard form.

Now, let's work through each step:
Step 1: Start with the expression given in the problem:
$(x + 4)^2 = x^2 + 2 \cdot x \cdot 4 + 4^2$.

This results in:
$x^2 + 8x + 16$.

Step 2: Subtract 16 from the expanded expression:
$x^2 + 8x + 16 - 16 = x^2 + 8x$.

Step 3: The standard form of the expression is now:
$f(x) = x^2 + 8x$.

Therefore, the standard representation of the function is $f(x) = x^2 + 8x$.