Question

What is the ordered pair of when I equals 1/3 x squared - 2
Free, -1 3, 3 3, 0 3, 1

Answer 1

To find the ordered pair for the equation \( I = \frac{1}{3}x^2 - 2 \), we can test the provided values of \( x \) to find the corresponding value of \( I \):

1. For \( x = -1 \):
\[
I = \frac{1}{3}(-1)^2 - 2 = \frac{1}{3}(1) - 2 = \frac{1}{3} - 2 = \frac{1}{3} - \frac{6}{3} = -\frac{5}{3}
\]

2. For \( x = 3 \):
\[
I = \frac{1}{3}(3)^2 - 2 = \frac{1}{3}(9) - 2 = 3 - 2 = 1
\]

3. For \( x = 0 \):
\[
I = \frac{1}{3}(0)^2 - 2 = 0 - 2 = -2
\]

4. For \( x = 1 \):
\[
I = \frac{1}{3}(1)^2 - 2 = \frac{1}{3}(1) - 2 = \frac{1}{3} - 2 = \frac{1}{3} - \frac{6}{3} = -\frac{5}{3}
\]

Now let's summarize these results and check which of the ordered pairs could be correct based on the calculated values:

- For \( x = -1 \), \( I = -\frac{5}{3} \)
- For \( x = 3 \), \( I = 1 \)
- For \( x = 0 \), \( I = -2 \)
- For \( x = 1 \), \( I = -\frac{5}{3} \)

None of the provided values (free, -1, 3, 0, 1) correspond to valid \( I \) outputs based on what we have computed. It's possible the "Free" value refers to any input across the equation, in which case it can match different outputs depending on \( x \).

If you want to find the specific ordered pairs based on the results, the following points are valid:

1. \( (-1, -\frac{5}{3}) \)
2. \( (3, 1) \)
3. \( (0, -2) \)
4. \( (1, -\frac{5}{3}) \)

If "Free" implies any input value, then any \( x \) could lead to a unique \( I \) as per the function provided.

Make sure to clarify which specific value or ordered pair you're looking for!