Math Problem Statement

Using the graph, determine the equation of the axis of symmetry.

Solution

The graph provided shows a parabola that opens upwards. The axis of symmetry of a parabola can be found by determining the x-coordinate of the vertex, which is the highest or lowest point on the graph, depending on the direction of the parabola.

Looking at the graph, the vertex of the parabola appears to be at the point (2,9)(-2, -9), since this is the lowest point on the graph. The axis of symmetry is a vertical line that passes through the vertex.

Thus, the equation of the axis of symmetry is: x=2x = -2

Would you like further explanation or additional details?

Here are 5 related questions for further exploration:

  1. How can we find the axis of symmetry algebraically for any quadratic function?
  2. What is the significance of the vertex in the graph of a parabola?
  3. Can the axis of symmetry be used to determine other properties of the parabola, such as the focus and directrix?
  4. How do the coefficients of a quadratic equation affect the position of the vertex and axis of symmetry?
  5. What other ways can we verify the accuracy of the vertex from the graph?

Tip: The axis of symmetry always passes through the vertex of a parabola and divides it into two mirror-image halves.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Graphing Parabolas

Formulas

Axis of symmetry formula: x = -b / 2a

Theorems

Symmetry of Parabolas

Suitable Grade Level

Grades 8-10