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The intersection points, where \( f(x) = g(x) \), are approximately:

1. \( x = -1 + \frac{\sqrt{10}}{2} \approx -0.42 \)
2. \( x = -1 - \frac{\sqrt{10}}{2} \approx -2.58 \)

### Answers for each part:
- **(a)** The values of \( x \) for which \( f(x) = g(x) \) are approximately \( x \approx -0.42 \) and \( x \approx -2.58 \).
- **(b)** For \( f(x) \geq g(x) \), the intervals can be estimated from the graph. It appears that \( f(x) \geq g(x) \) when \( x \in [-3, -2.58] \cup [-0.42, 2] \).

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Use the same scales and axes to draw the graphs of the two functions f(x) = 2 + 2x + x^2 and g(x) = 5 - 2x - x^2 in the domain -3 ≤ x ≤ 2, x ∈ R. (a) Use your graphs to estimate the values of x for which f(x) = g(x). (b) Use your graphs to estimate the values of x for which f(x) ≥ g(x).

Explore how to graph and analyze the functions f(x) = 2 + 2x + x^2 and g(x) = 5 - 2x - x^2 over the domain -3 ≤ x ≤ 2. Learn how to estimate intersection points and determine intervals where f(x) ≥ g(x). Suitable for high school students studying algebra and quadratic functions.

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