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Here is the graph of the function \( f(x) = 2 + 3x^2 \). The parabola opens upwards, with its vertex at \( (0, 2) \) and increasing steeply due to the coefficient of \(x^2\) being 3. 

Would you like more details or have any specific questions?

Here are some related questions to explore further:
1. How does the value of the coefficient 3 affect the steepness of the parabola?
2. What would happen to the graph if we change the constant term (2) to a different value?
3. How would the graph change if we introduced a linear term like \( bx \) in the equation?
4. Can you determine the axis of symmetry for this graph?
5. How do you find the roots of this quadratic function?

**Tip:** The vertex form of a quadratic function provides an easy way to identify the vertex, making graphing simpler.

Explore the graph of the quadratic function f(x) = 2 + 3x^2, including details on the vertex, axis of symmetry, and how the coefficient affects the steepness of the parabola. Suitable for students in Grades 9-11.

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