Question

ready make a point on the vertex, and draw a dotted line for the line of symmetry. label the coordinates of the vertex, and state whether its a maximum or a minimum. write the equation for the line of symmetry. 1. 2. 3. 4. 5. 6.

Explanation:

Step1: Identify vertex

The vertex is the highest or lowest point of the parabola. For an upward - opening parabola, it's the minimum; for a downward - opening parabola, it's the maximum.

Step2: Determine line of symmetry

The line of symmetry of a parabola passes through the vertex. For a parabola in the form \(y = ax^{2}+bx + c\), the equation of the line of symmetry is \(x=-\frac{b}{2a}\), and for a graph, it's the vertical line through the vertex.

Problem 1

• Vertex: \((0,0)\)
• Since the parabola opens upward, it's a minimum.
• Equation of line of symmetry: \(x = 0\)

Problem 2

• Vertex: \((3,1)\) (estimated from the graph)
• Since the parabola opens upward, it's a minimum.
• Equation of line of symmetry: \(x=3\)

Problem 3

• Vertex: \((0, - 2)\)
• Since the parabola opens upward, it's a minimum.
• Equation of line of symmetry: \(x = 0\)

Problem 4

• Vertex: \((-2,4)\) (estimated from the graph)
• Since the parabola opens downward, it's a maximum.
• Equation of line of symmetry: \(x=-2\)

Problem 5

• Vertex: \((0,3)\)
• Since the parabola opens downward, it's a maximum.
• Equation of line of symmetry: \(x = 0\)

Problem 6

• Vertex: \((2,-3)\) (estimated from the graph)
• Since the parabola opens upward, it's a minimum.
• Equation of line of symmetry: \(x = 2\)

Answer:

1. Vertex: \((0,0)\), Minimum, Line of symmetry: \(x = 0\)
2. Vertex: \((3,1)\), Minimum, Line of symmetry: \(x=3\)
3. Vertex: \((0,-2)\), Minimum, Line of symmetry: \(x = 0\)
4. Vertex: \((-2,4)\), Maximum, Line of symmetry: \(x=-2\)
5. Vertex: \((0,3)\), Maximum, Line of symmetry: \(x = 0\)
6. Vertex: \((2,-3)\), Minimum, Line of symmetry: \(x = 2\)