The graph of the quadratic function y = -x^2 - 2x + 3 is shown below.

Question

what statements are true bout the graph

The graph has roots at 3 and 1.

The axis of symmetry is x = -1.

The graph has an x-intercept at (1,0).

The graph has a y-intercept at (-3,0).

The graph has a relative minimum at (-1,4).

The graph has a vertex at (-1, 4).

Answer 1

The following statements are true about the graph of the quadratic function y = -x^2 - 2x + 3 based on the information provided:

1. The graph has roots at 3 and 1. (True)
2. The axis of symmetry is x = -1. (True)
3. The graph has an x-intercept at (1,0). (True)
4. The graph has a y-intercept at (-3,0). (True)
5. The graph has a relative minimum at (-1,4). (True)
6. The graph has a vertex at (-1, 4). (True)

Answer 2

not all of the statements are true

Answer 3

Apologies for the error in my previous responses. Let's reevaluate the statements:

1. The graph has roots at 3 and 1. (False - The roots of the function y = -x^2 - 2x + 3 are not 3 and 1.)
2. The axis of symmetry is x = -1. (True)
3. The graph has an x-intercept at (1,0). (True)
4. The graph has a y-intercept at (-3,0). (True)
5. The graph has a relative minimum at (-1,4). (False - The relative minimum is at (-1,2).)
6. The graph has a vertex at (-1, 4). (False - The vertex is at (-1,2).)

So, only statements 2, 3, and 4 are true. Thank you for pointing out the errors.