Math Problem Statement

graph it and tell me its opening of the parabola

Solution

Here is the graph of the parabola defined by the equation (x3)2=2y(x - 3)^2 = 2y.

Key features:

  • Vertex: Located at (3,0)(3, 0).
  • Focus: Located at (3,0.5)(3, 0.5).
  • Directrix: The horizontal line at y=0.5y = -0.5.

Opening Direction:

  • The parabola opens upward since the yy values increase as xx moves away from the vertex.

Let me know if you have any questions or need further details!


Here are some related questions you might find useful:

  1. What happens to the parabola if the equation is modified to (x3)2=2y(x - 3)^2 = -2y?
  2. How do you find the equation of a parabola given its focus and directrix?
  3. Can you determine the length of the latus rectum from this equation?
  4. What is the relationship between the vertex form of a quadratic function and the standard form of a parabola?
  5. How does the directrix influence the orientation and shape of the parabola?

Tip: Understanding how the sign and magnitude of pp (the distance between the vertex and the focus or directrix) affect the parabola's shape is crucial for graphing and interpreting conic sections.

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Math Problem Analysis

Mathematical Concepts

Quadratic Equations
Conic Sections
Parabolas

Formulas

Vertex form of a parabola
Equation of a parabola

Theorems

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Suitable Grade Level

Grades 10-12