Math Problem Statement

Put a dot on the vertex of the parabola below. What is the coordinates of the vertex? Is the vertex a minimum or maximum?

Solution

The graph shown in the image represents a downward-opening parabola. The vertex of the parabola is its highest point because the parabola opens downward.

From the graph, we can visually identify the vertex as occurring at the point where the curve reaches its peak. Based on the plot, the vertex appears to be at the point (2,3)(2, 3).

Answer:

  • The coordinates of the vertex are (2,3)(2, 3).
  • Since the parabola opens downward, the vertex represents a maximum point.

Would you like more details or further explanations on this topic?

Follow-up Questions:

  1. How can you determine if a parabola has a minimum or maximum without graphing?
  2. What is the formula for finding the vertex of a parabola given in standard form?
  3. How does the sign of the leading coefficient in a quadratic equation affect the direction of the parabola?
  4. Can you convert a quadratic equation from vertex form to standard form?
  5. How can you use the vertex to write the equation of a parabola in vertex form?

Tip:

The vertex form of a parabola y=a(xh)2+ky = a(x-h)^2 + k makes it easy to find the vertex, which is (h,k)(h, k).

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Parabolas
Graphing

Formulas

Vertex form of a parabola y = a(x-h)^2 + k

Theorems

Properties of Parabolas
Maximum and Minimum of Quadratic Functions

Suitable Grade Level

Grades 9-12