Solve for X in y=x²: Finding X-Coordinates When y=8

The problem requires us to find the value of $x$ for the function $y = x^2$ when $y = 8$.

Let's solve this step-by-step:

• Step 1: Set up the equation based on the given function:
  $\ y = x^2$ becomes $\ x^2 = 8$.
• Step 2: Solve for $x$ by taking the square root of both sides:

Since $\ x^2 = 8$, we take the square root of both sides to find $x$:

$x = \pm\sqrt{8}$

Step 3: Simplify the square root:

The square root of 8 can be simplified to $\ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}$.

Thus, $\ x = \pm 2\sqrt{2}$.

Therefore, the solution is $x = \pm 2\sqrt{2}$, which corresponds to choice 4.