To determine which graph matches the given description of the parabola, we need to analyze the properties provided:
1. Maximum Value of 4 at [tex]\( x = -1 \)[/tex]:
This tells us that the vertex of the parabola is at the point [tex]\((-1, 4)\)[/tex]. Since this is a maximum value, the parabola opens downwards.
2. [tex]\( y \)[/tex]-Intercept of 3:
This means the parabola intersects the y-axis at the point [tex]\((0, 3)\)[/tex].
3. [tex]\( x \)[/tex]-Intercept of 1:
This indicates that the parabola intersects the x-axis at the point [tex]\((1, 0)\)[/tex].
Let's summarize these key points:
- Vertex: [tex]\((-1, 4)\)[/tex]
- Opens Downwards: The parabola reaches a maximum value at its vertex.
- [tex]\( y \)[/tex]-Intercept: [tex]\((0, 3)\)[/tex]
- [tex]\( x \)[/tex]-Intercept: [tex]\((1, 0)\)[/tex]
Now, let's discuss how these properties would reflect on the graph:
- Since the vertex is at [tex]\((-1, 4)\)[/tex] and the parabola opens downwards, we expect a curve that peaks at this point.
- The parabola will cross the y-axis at [tex]\((0, 3)\)[/tex]. Visually, this is a point along the vertical line [tex]\(x = 0\)[/tex].
- The parabola will cross the x-axis at [tex]\((1, 0)\)[/tex]. This is where the curve intersects the horizontal axis.
Using these details, identify the graph that satisfies all three conditions. The correct graph should:
1. Peak at [tex]\((-1, 4)\)[/tex].
2. Cross the y-axis at [tex]\((0, 3)\)[/tex].
3. Cross the x-axis at [tex]\((1, 0)\)[/tex].
Check which graph carefully reflects these points and properties accurately.
Thus, based on the provided data, select the graph that correctly displays a parabola with its maximum value at [tex]\((-1, 4)\)[/tex], a y-intercept at [tex]\((0, 3)\)[/tex], and an x-intercept at [tex]\((1, 0)\)[/tex].
