Math Problem Statement

Find the vertex and the equation of the axis of symmetry for the given parabola.

Solution

The image shows a parabola. Let's analyze the important features of this graph.

1. Vertex:

The vertex of a parabola is the highest or lowest point on the graph. In this case, the vertex appears to be at the point (2, 1).

2. Equation of Axis of Symmetry:

The axis of symmetry is a vertical line that divides the parabola into two symmetrical parts. Since the vertex is at x=2x = 2, the equation of the axis of symmetry is x=2x = 2.

Summary:

  • Vertex: (2, 1)
  • Equation of Axis of Symmetry: x=2x = 2

Would you like further clarification or more details? Here are some related questions that may be helpful:

  1. What is the general equation of a parabola in vertex form?
  2. How do you find the direction of opening for a parabola?
  3. What is the importance of the axis of symmetry in quadratic functions?
  4. How does the value of "a" in a quadratic equation affect the shape of the parabola?
  5. How can you graph a parabola given the vertex and axis of symmetry?

Tip: The axis of symmetry always passes through the vertex, and its equation is always in the form x=hx = h, where (h,k)(h, k) is the vertex of the parabola.

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Math Problem Analysis

Mathematical Concepts

Parabolas
Quadratic Functions
Symmetry

Formulas

Vertex form of a parabola: y = a(x - h)^2 + k
Axis of symmetry: x = h

Theorems

Properties of parabolas
Axis of symmetry theorem

Suitable Grade Level

Grades 8-10