Math Problem Statement

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

Solution

The graph in the image shows a parabola opening upwards. To find the equation of the axis of symmetry, we need to determine the x-coordinate of the vertex of the parabola. The axis of symmetry is always a vertical line that passes through the vertex.

From the graph, it appears that the vertex is located at x=4x = -4. Therefore, the equation of the axis of symmetry is:

x=4x = -4

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Related Questions:

  1. What is the vertex form of a parabola and how is it useful in finding the axis of symmetry?
  2. How can you determine the vertex of a parabola from a quadratic equation?
  3. What are the steps to graph a parabola if you're only given its equation?
  4. How does the direction of the parabola (opening up or down) affect its vertex?
  5. What is the significance of the axis of symmetry in relation to the properties of a parabola?

Tip:

The axis of symmetry is always given by x=hx = h, where hh is the x-coordinate of the vertex in the vertex form of a quadratic equation: y=a(xh)2+ky = a(x - h)^2 + k.

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Math Problem Analysis

Mathematical Concepts

Parabola
Axis of Symmetry
Quadratic Graphs

Formulas

x = h, where h is the x-coordinate of the vertex in y = a(x - h)^2 + k

Theorems

The Axis of Symmetry Theorem for Parabolas

Suitable Grade Level

Grades 9-10