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