ANSWER
Option B: (0, 0) satisifes y >= x^2 + x - 4 while it does not satisfy y > x^2 + 2x + 1
EXPLANATION
We are given two inequalities:
[tex]\begin{gathered} y\text{ }\ge x^2\text{ + x - 4} \\ y>x^2\text{ + }2x\text{ + 1} \end{gathered}[/tex]
To check if (0, 0) satisifes both inequalities, we have to put the values of x and y as 0 and see if the resulting inequality is mathematically correct.
We have that:
[tex]\begin{gathered} 0\text{ }\ge0^2\text{ + 0 - 4} \\ \Rightarrow\text{ 0 }\ge\text{ -4} \\ \text{and} \\ 0>0^2\text{ + 2(0) + 1} \\ 0\text{ > 1} \end{gathered}[/tex]
As we can see, (0, 0) satisifes the first inequality while it does not satisfy the second one.
The answer is Option B
