Math Problem Statement

gambarkan saya grafik a. x=-√4-y² b. x=3+√4-y²

Solution

Here is the graph of the two equations:

a. x=4y2x = -\sqrt{4 - y^2} (in blue)
b. x=3+4y2x = 3 + \sqrt{4 - y^2} (in red)

These equations form semicircles. The first equation (blue) is positioned to the left of the origin, while the second (red) is shifted to the right by 3 units.

Do you need any details or explanations about these graphs?

Here are 5 related questions for further exploration:

  1. What are the domain and range for each equation?
  2. How do transformations affect the shape and position of these curves?
  3. Can you describe how the curves change if the coefficients inside the square roots are modified?
  4. What would happen if we squared both sides of the equations?
  5. How would you describe these shapes in a real-world context?

Tip: For graphing equations with square roots, always check the domain restrictions to avoid plotting undefined points.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Graphing
Semicircles
Square Root Functions

Formulas

x = -√(4 - y²)
x = 3 + √(4 - y²)

Theorems

Transformation of functions
Domain and Range

Suitable Grade Level

Grades 10-12