Math Problem Statement

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

Solution

To determine the axis of symmetry from the graph:

  1. The axis of symmetry of a parabola is a vertical line that passes through its vertex.
  2. From the graph, the vertex of the parabola appears to be at x=2x = -2.
  3. Therefore, the equation for the axis of symmetry is: x=2x = -2

Would you like more details on the concept of the axis of symmetry, or do you have any questions?

Here are some related questions you might consider:

  1. What is the importance of the axis of symmetry in a quadratic function?
  2. How would you find the vertex of a parabola if given its equation?
  3. Can the axis of symmetry be horizontal? Why or why not?
  4. How can you determine the axis of symmetry if the graph is not available, but the equation is?
  5. How does the axis of symmetry relate to the solutions (roots) of a quadratic equation?

Tip: For any quadratic equation in the form y=ax2+bx+cy = ax^2 + bx + c, the axis of symmetry can be found using the formula x=b2ax = -\frac{b}{2a}.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Axis of Symmetry

Formulas

Axis of symmetry formula: x = -b/(2a) for y = ax^2 + bx + c

Theorems

The Axis of Symmetry Theorem for Parabolas

Suitable Grade Level

Grades 9-10