Math Problem Statement

What is the vertex of the parabola shown in the graph?

Solution

From the image you provided, it appears you are working on a multiple-choice question related to identifying the vertex of a parabola. The graph shows a parabola opening upwards, and the vertex is the lowest point on the graph.

Looking closely at the graph, the vertex seems to occur at the point (3,1)(3, -1). Therefore, the correct answer to the question "What is the vertex?" would be:

(3, -1)

Would you like more details on how to determine the vertex from a graph?

Here are five related questions:

  1. How do you find the vertex from the equation of a parabola?
  2. What is the axis of symmetry of a parabola?
  3. How can you determine if a parabola opens upwards or downwards?
  4. How does the vertex relate to the maximum or minimum point of a parabola?
  5. Can the vertex be calculated from the standard quadratic form ax2+bx+cax^2 + bx + c?

Tip: The vertex form of a parabola’s equation is y=a(xh)2+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex.

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Math Problem Analysis

Mathematical Concepts

Parabolas
Quadratic Functions
Vertex

Formulas

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

Theorems

The vertex of a parabola is the minimum or maximum point
Axis of symmetry passes through the vertex

Suitable Grade Level

Grades 8-10