Find the Positive Area: Solving y=(x+5)² Above the X-axis

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

• Step 1: Identify where the quadratic expression $(x+5)^2$ equals zero, as this determines when $y=0$.
• Step 2: Solve the equation $(x+5)^2 = 0$ to find values of $x$.
• Step 3: Determine the values of $x$ where $(x+5)^2 > 0$.

Now, let's work through each step:

Step 1: We need to analyze the expression $(x+5)^2$.

Step 2: Solve $(x+5)^2 = 0$.
The equation simplifies to:

$(x+5) = 0$
Solve for $x$:
$x = -5$

Step 3: Determine $x$ values where $(x+5)^2$ is positive.
The expression $(x+5)^2$ is positive for any $x \neq -5$, because the square of a non-zero real number is always positive.

Therefore, the quadratic $(x+5)^2$ is positive for $x \neq -5$, meaning the positive area applies for all $x$ except $x = -5$.

The correct choice is: For each $x \neq -5$.

Therefore, the solution to the problem is For each $x \neq 5$.