Solving y = x²: Finding Points Where y = -6

Given the function:

$y=x^2$

Is there a point for ? $y=-6$?

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

• Step 1: Identify the given function and required y-value.
• Step 2: Attempt to solve $x^2 = -6$ for $x$.
• Step 3: Conclude based on the results of the equation.

Let's work through each step:

Step 1: The function we are dealing with is $y = x^2$, and we need to find $x$ such that $y = -6$.

Step 2: Substitute $-6$ for $y$, which gives us:

$x^2 = -6$

Step 3: To solve $x^2 = -6$, consider whether it is possible for a real number squared to equal a negative number. A critical point here is that the square of any real number is non-negative. Therefore, there is no real value of $x$ that satisfies $x^2 = -6$.

Thus, there is no point where $y = -6$ for the function $y = x^2$.

The correct answer is No.