graph the function. Given the domain and range f(x)=xsquared+2

Here is the graph of the function \( f(x) = x^2 + 2 \). The parabola has its vertex at \( (0, 2) \), and it opens upwards. The domain is \( (-\infty, \infty) \), and the range is \( [2, \infty) \).

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### Related Questions:
1. How would the graph change if the function were \( f(x) = x^2 - 3 \)?
2. What is the effect of changing the constant 2 to 5 in \( f(x) = x^2 + 5 \)?
3. How do you find the vertex of any quadratic function?
4. What are the roots (if any) of the function \( f(x) = x^2 + 2 \)?
5. How does the graph change if the coefficient of \( x^2 \) becomes negative?

### Tip:  
For any quadratic function \( f(x) = ax^2 + bx + c \), the vertex can be found using \( x = -\frac{b}{2a} \).

Explore the graph of the quadratic function f(x) = x^2 + 2. Learn about its domain, range, and vertex, and understand how changes to the equation affect the graph. Suitable for students in Grades 8-10.

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