Math Problem Statement

What are the coordinates of the vertex?

Solution

The graph shows a parabola opening upwards, which indicates it has a minimum point at the vertex. Observing the graph, the vertex appears to be at the point (0,5)(0, -5).

So, the coordinates of the vertex are: (0,5)(0, -5)

Would you like a detailed explanation of this?

Here are some related questions for further exploration:

  1. How do you determine the vertex of a parabola given its equation?
  2. What is the significance of the vertex in a quadratic function?
  3. How can you identify the axis of symmetry from the graph of a parabola?
  4. How do changes in the quadratic equation affect the position of the vertex?
  5. What is the general form of a quadratic function, and how can we use it to find the vertex?

Tip: In a parabola y=ax2+bx+cy = ax^2 + bx + c, the x-coordinate of the vertex can be calculated using x=b2ax = -\frac{b}{2a}.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Vertex of a Parabola

Formulas

Vertex form of a parabola: y = ax^2 + bx + c

Theorems

Properties of Quadratic Functions

Suitable Grade Level

Grades 8-10