Math Problem Statement

Identify the vertex of the graph.

Solution

The graph in the image shows a parabola, and you are asked to identify its vertex. The vertex of a parabola is the point where it changes direction, which is either its lowest or highest point depending on the orientation.

From the graph, the parabola opens upwards, so the vertex is the lowest point. The vertex appears to be located at the point (2,6)(-2, -6) where the graph reaches its minimum.

Vertex: (2,6)(-2, -6)

Would you like further details or have any questions?

Here are some related questions for practice:

  1. What is the axis of symmetry for the given parabola?
  2. How do you find the equation of the parabola from the vertex?
  3. What is the significance of the vertex in real-world applications?
  4. How can you determine if a parabola opens upwards or downwards by looking at its equation?
  5. What are the x-intercepts of this graph?

Tip: The vertex form of a quadratic function is useful in easily identifying the vertex from an equation.

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Math Problem Analysis

Mathematical Concepts

Quadratic Functions
Vertex of a Parabola
Graphing Parabolas

Formulas

Vertex form of a quadratic function: y = a(x - h)^2 + k
General form of a quadratic equation: ax^2 + bx + c

Theorems

The vertex of a parabola is the point (h, k) when expressed in vertex form.

Suitable Grade Level

Grades 9-11