4. Which of the following points lies on the graph of \( y=x^{2}-5 \) ? \( \begin{array}{ll}\text { (1) }(3,-2) & \text { (3) }(5,0) \\ \text { (2) }(-2,-1) & \text { (4) }(-1,-6)\end{array} \)

To determine which points lie on the graph of the equation \( y = x^2 - 5 \), we will substitute the \( x \)-coordinate of each point into the equation and check if the resulting \( y \)-value matches the \( y \)-coordinate of the point. Let's evaluate each point one by one: 1. For the point \( (3, -2) \): \[ y = 3^2 - 5 = 9 - 5 = 4 \] The point \( (3, -2) \) does not lie on the graph since \( -2 \neq 4 \). 2. For the point \( (-2, -1) \): \[ y = (-2)^2 - 5 = 4 - 5 = -1 \] The point \( (-2, -1) \) lies on the graph since \( -1 = -1 \). 3. For the point \( (5, 0) \): \[ y = 5^2 - 5 = 25 - 5 = 20 \] The point \( (5, 0) \) does not lie on the graph since \( 0 \neq 20 \). 4. For the point \( (-1, -6) \): \[ y = (-1)^2 - 5 = 1 - 5 = -4 \] The point \( (-1, -6) \) does not lie on the graph since \( -6 \neq -4 \). After evaluating all points, we find that the only point that lies on the graph of \( y = x^2 - 5 \) is: **Point (2): \( (-2, -1) \)**.