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

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

UpStudy AI · Accepted Answer

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): $$ (-2, -1) $$**.
Point (2) $$ (-2, -1) $$ lies on the graph of $$ y = x^2 - 5 $$.

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

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