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Here is the graph of the function \( F(x) = -2x^2 + 1 \). As you can see, it represents a downward-opening parabola because the coefficient of \( x^2 \) is negative. The vertex of the parabola is at \( (0, 1) \), which is the maximum point on the graph.

Would you like further explanation on any aspect of this graph?

Here are some related questions:
1. How can you find the vertex of a quadratic function?
2. What effect does the coefficient of \( x^2 \) have on the shape of the parabola?
3. How do we find the roots (x-intercepts) of this quadratic equation?
4. What is the range of the function \( F(x) = -2x^2 + 1 \)?
5. How does this graph change if the constant term \( +1 \) is modified?

**Tip**: The vertex form of a quadratic function \( F(x) = a(x-h)^2 + k \) can help in quickly identifying the vertex and transformations.

grafica la siguiente función F(x) = -2x^2 + 1

Learn how to graph the quadratic function F(x) = -2x^2 + 1, focusing on the properties of parabolas, identifying the vertex, and understanding the effect of the negative coefficient on the graph's shape. Ideal for students in Grades 9-12.

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