Answer:
In summary:
- Axis of symmetry: Not determinable from the given information.
- X-intercepts: (-1, 0) and (1.5, 0).
- Y-intercept: Not determinable from the given information.
- Vertex: (-1, 4).
- Interval of decrease: (-∞, -1) and (1.5, ∞).
Explanation:
To identify the axis of symmetry, x-intercepts, y-intercept, and vertex of a graph, we need to analyze the given information and graph:
1. Axis of symmetry: The axis of symmetry is a vertical line that divides the graph into two symmetric halves. It is represented by the equation x = h, where h is the x-coordinate of the vertex. Based on the given information, we don't have the equation of the graph or the value of h, so we cannot determine the axis of symmetry.
2. X-intercepts: X-intercepts are the points where the graph intersects the x-axis. These points have a y-coordinate of 0. From the given information, we have the x-intercepts as follows:
- First x-intercept: (-1, 0)
- Second x-intercept: (1.5, 0)
3. Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It has an x-coordinate of 0. From the given information, we don't have the y-intercept, so we cannot determine its value.
4. Vertex: The vertex is the highest or lowest point on the graph. It has an x-coordinate and a y-coordinate. From the given information, we have the vertex as follows:
- Vertex: (-1, 4)
Now, let's determine the interval in which the function is decreasing. To do this, we need to analyze the graph and observe where the graph is sloping downwards or decreasing. From the given information, we can see that the graph is decreasing in the interval (-∞, -1) and in the interval (1.5, ∞). These intervals represent the regions on the x-axis where the function is decreasing.