Finding the Parts of a Parabola | CK-12 Foundation - Free Printable

Problem Analysis:

The image shows a parabola (a quadratic function) on a coordinate grid. The key features labeled in the image are:
1. Axis of Symmetry: A vertical line that divides the parabola into two symmetric halves.
2. x-Intercepts (Solutions): The points where the parabola intersects the x-axis.
3. y-Intercept: The point where the parabola intersects the y-axis.
4. Vertex: The lowest or highest point of the parabola, depending on its orientation.

The task is to identify and explain these features based on the given graph.

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Step-by-Step Solution:

#### 1. Axis of Symmetry
- The axis of symmetry is a vertical line that passes through the vertex of the parabola.
- From the graph, the vertex is located at the point \((1, -4)\).
- The axis of symmetry is therefore the vertical line \(x = 1\).

#### 2. x-Intercepts (Solutions)
- The x-intercepts are the points where the parabola crosses the x-axis. At these points, the value of \(y\) is zero.
- From the graph, the parabola intersects the x-axis at two points:
- One point is at \((-1, 0)\).
- The other point is at \((3, 0)\).
- Therefore, the x-intercepts are \((-1, 0)\) and \((3, 0)\).

#### 3. y-Intercept
- The y-intercept is the point where the parabola crosses the y-axis. At this point, the value of \(x\) is zero.
- From the graph, the parabola intersects the y-axis at the point \((0, -3)\).
- Therefore, the y-intercept is \((0, -3)\).

#### 4. Vertex
- The vertex is the lowest or highest point of the parabola. In this case, since the parabola opens upwards, the vertex is the lowest point.
- From the graph, the vertex is clearly marked at the point \((1, -4)\).

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Final Answer:

Summarizing the key features:
- Axis of Symmetry: \(x = 1\)
- x-Intercepts (Solutions): \((-1, 0)\) and \((3, 0)\)
- y-Intercept: \((0, -3)\)
- Vertex: \((1, -4)\)

$$
\boxed{x = 1, (-1, 0) \text{ and } (3, 0), (0, -3), (1, -4)}
$$