Although it helps, we don't need to know the actual shapes of the two parabolas.

Key property: \(k^2 \geq 0\) for all values of \(k\)
In other words, \(k^2\) is greater than or equal to 0 for all values of k

Quantity A: minimum y coordinate value of Point P
Since P is a point on the parabola, its coordinates must satisfy the parabola's equation \(y=x^2−1\)
So, to find the minimum value of \(y\), we are really finding the minimum value of \(x^2 - 1\)
Since \(x^2 \geq 0\) for all values of \(x\), the minimum of \(x^2 \geq 0\) is 0, which means the minimum value of \(x^2−1\) is 0 - 1 = -1

Quantity B: maximum y coordinate value of Point Q
Applying the same logic, we know that the coordinates of point Q must satisfy the equation \(y=−x^2+1\), which we can also write as \(y=−(x^2)+1\)
Key property: \(-(k^2) \leq 0\) for all values of \(k\)
So, to find the maximum value of \(y\), we are really finding the maximum value of \(-(x^2)+1\)
Since the maximum value of \(-(x^2)\) is 0, we know the maximum value of \(-(x^2)+1\) is 0 + 1 = 1

So, we have:
Quantity A: -1
Quantity B: 1

Answer: B