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graph parabola in vertex form showing intercepts and visual graph

Here is the visual representation of the parabola given by the equation \( y = -(x - 1)^2 + 3 \). It shows the vertex, intercepts, and the shape of the parabola.

If you have any further questions or need additional details, feel free to ask!

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### Related Questions:

1. How does the vertex form of a quadratic equation help in graphing parabolas?
2. What are the effects of the sign of the coefficient \(a\) on the direction of the parabola?
3. How can you find the equation of a parabola given its vertex and a point on the graph?
4. How does completing the square convert a quadratic equation into vertex form?
5. What is the significance of the discriminant in finding the x-intercepts of a parabola?
6. How do transformations like translations and reflections affect the graph of a parabola?
7. What are the steps to graph a parabola given in standard form?
8. How do you determine the domain and range of a parabola?

**Tip:** For quick sketching, remember that the vertex form provides direct information about the vertex, and the coefficient of \( (x - h)^2 \) indicates whether the parabola opens upwards or downwards.

Learn how to graph a parabola in vertex form, including intercepts and the visual representation of the equation y = -(x - 1)^2 + 3. This detailed guide covers key concepts in quadratic equations and graphing. Suitable for high school students.

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