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The image shows three mathematical problems asking for graphing specific equations. Here's a breakdown:

1. **\( x = y^2 + 4 \)**: This is a parabolic equation, representing a parabola that opens horizontally (right or left) because the variable \(x\) is expressed in terms of \(y\).

2. **\( xy = 1 \)**: This is a hyperbola, as it describes the reciprocal relationship between \(x\) and \(y\).

3. **\( x^2 - 4x + 3y^2 = -2 \)**: This is a conic section equation that can be rewritten and simplified. It represents either an ellipse or hyperbola depending on the terms' values and signs after simplification.

Would you like help plotting these graphs or simplifying the third equation?

Here are 5 related questions:

1. How can you determine the vertex of a parabola in the form \(x = y^2 + 4\)?
2. What are the key characteristics of hyperbolas from the equation \(xy = 1\)?
3. How can you complete the square to analyze the conic \(x^2 - 4x + 3y^2 = -2\)?
4. What role do conic sections play in understanding curves in geometry?
5. How does the orientation of a parabola change depending on the variable?

**Tip:** Always check whether an equation can be simplified or rewritten in standard form to make graphing easier!

Gambarkan grafik persamaan: 1. x = y^2 + 4 2. xy = 1 3. x^2 - 4x + 3y^2 = -2.

Learn how to graph the equations of parabolas, hyperbolas, and conic sections. This problem involves solving and graphing the equations x = y^2 + 4, xy = 1, and x^2 - 4x + 3y^2 = -2. Ideal for high school students.

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