Solving y = x²: Does a Point Exist Where y = -2?

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

• Step 1: Analyze the equation $y = x^2$.
• Step 2: Investigate whether a negative $y$-value is possible.

Now, let's work through each step:
Step 1: The function we have is $y = x^2$. This function is defined for all real numbers and always gives a non-negative value $y$ because squaring a real number cannot result in a negative number.

Step 2: We need to check whether $y = -2$ is possible by solving $x^2 = -2$. In the real number system, no real number $x$ satisfies this equation since the square of any real number is non-negative.
Therefore, there is no real point where $y = -2$ on the graph of the function $y = x^2$.

Therefore, the solution to the problem is No.