Math Problem Statement

What are the coordinates of the vertex of the parabola shown in the graph?

Solution

The given graph is a parabola that opens upwards. The vertex of a parabola is its lowest or highest point.

From the image, the vertex is located at the point where the curve reaches its minimum. Observing the graph, the vertex is at (0,5)(0, -5).

Answer:

The coordinates of the vertex are (0,5)(0, -5).

Would you like a detailed explanation on how to determine the vertex of a quadratic function?

Related Questions:

  1. How do you find the vertex of a quadratic function algebraically?
  2. What is the general form of a quadratic equation?
  3. How do you determine if a parabola opens upward or downward?
  4. How do you convert a quadratic equation from standard form to vertex form?
  5. What is the significance of the axis of symmetry in a parabola?

Tip:

The vertex of a quadratic function in standard form y=ax2+bx+cy = ax^2 + bx + c is found using the formula x=b2ax = -\frac{b}{2a}. Then, substitute xx into the equation to find yy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Vertex of a Parabola

Formulas

x = -b/(2a) for the vertex of a quadratic function in standard form

Theorems

Vertex Formula Theorem

Suitable Grade Level

Grades 7-9