Looking at Graph 4, I can see a parabola that opens downwards. The vertex appears to be at the point (-1, 5). The graph crosses the x-axis at two points: approximately x = -3 and x = 1. It crosses the y-axis at y = 3.
Based on this visual analysis:
- Domain: All real numbers, since the parabola extends infinitely left and right.
- Range: Since it opens downward with a vertex at y=5, the range is all y-values less than or equal to 5.
- x-intercepts: The points where the graph crosses the x-axis, which appear to be (-3, 0) and (1, 0).
- y-intercept: The point where the graph crosses the y-axis, which is (0, 3).
- Vertex: The highest point of the parabola, which is at (-1, 5).
- Maximum value: Since it opens downward, the maximum value is the y-coordinate of the vertex, which is 5.
- Axis of symmetry: A vertical line passing through the vertex, so x = -1.
- Open up or down: The parabola opens downward.
Now I will summarize all the findings for each graph.
Graph 1:
- Domain: All real numbers
- Range: $y \leq 1$
- x-intercepts: $(-3, 0)$ and $(-1, 0)$
- y-intercept: $(0, -3)$
- Vertex: $(-2, 1)$
- Maximum value: $1$
- Axis of symmetry: $x = -2$
- Opens: Down
Graph 2:
- Domain: All real numbers
- Range: $y \leq 2$
- x-intercepts: $(-2, 0)$ and $(2, 0)$
- y-intercept: $(0, 2)$
- Vertex: $(0, 2)$
- Maximum value: $2$
- Axis of symmetry: $x = 0$
- Opens: Down
Graph 3:
- Domain: All real numbers
- Range: $y \geq -1$
- x-intercepts: $(0, 0)$ and $(2, 0)$
- y-intercept: $(0, 0)$
- Vertex: $(1, -1)$
- Maximum value: None (opens upward)
- Axis of symmetry: $x = 1$
- Opens: Up
Graph 4:
- Domain: All real numbers
- Range: $y \leq 5$
- x-intercepts: $(-3, 0)$ and $(1, 0)$
- y-intercept: $(0, 3)$
- Vertex: $(-1, 5)$
- Maximum value: $5$
- Axis of symmetry: $x = -1$
- Opens: Down
Parent Tip: Review the logic above to help your child master the concept of characteristics of functions worksheet.
