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The text in the image reads:

"3. Gambarkan grafik persamaan \( x^2 - 4x + 3y^2 = -2 \)."

This equation is quadratic in both \( x \) and \( y \). To graph this equation, let's first analyze and convert it into a standard form.

### Step 1: Rewriting the Equation

We have the given equation:
\[
x^2 - 4x + 3y^2 = -2.
\]
We can complete the square for the \( x \)-terms to express it in a more recognizable form.

### Completing the square for \( x \):
\[
x^2 - 4x = (x - 2)^2 - 4.
\]
Now substitute this into the equation:
\[
(x - 2)^2 - 4 + 3y^2 = -2.
\]
Simplifying:
\[
(x - 2)^2 + 3y^2 = 2.
\]

### Step 2: Recognizing the Conic

This is now in the form of an ellipse equation:
\[
\frac{(x - 2)^2}{2} + \frac{y^2}{\frac{2}{3}} = 1.
\]

This represents an **ellipse** centered at \( (2, 0) \), with semi-major axis along the \( x \)-axis of length \( \sqrt{2} \) and semi-minor axis along the \( y \)-axis of length \( \sqrt{\frac{2}{3}} \).

### Step 3: Graphing the Equation

- Center: \( (2, 0) \)
- Horizontal radius: \( \sqrt{2} \)
- Vertical radius: \( \sqrt{\frac{2}{3}} \)

You can now sketch this ellipse with these properties.

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Would you like more details on the graphing process or any specific clarifications?

Here are 5 related questions to explore further:
1. How do you complete the square for quadratic terms?
2. What are the key features of an ellipse and how do they relate to the equation?
3. How does completing the square help in recognizing conic sections?
4. Can this equation represent a different conic section in other forms?
5. How do transformations like translation affect the graph of a conic section?

**Tip**: Completing the square is a useful technique for rewriting quadratic equations into standard forms, making it easier to recognize and graph conic sections!

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

Learn how to graph the ellipse from the equation x^2 - 4x + 3y^2 = -2 by completing the square and converting it into its standard form. This solution covers key concepts in quadratic equations and conic sections, ideal for students in Grades 9-12.

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