To determine how many times the graph of the function \( f(x) = x(x+2) \) crosses the x-axis, we need to find the values of \( x \) for which \( f(x) = 0 \).
We can set the function equal to zero:
\[ x(x + 2) = 0 \]
This equation will be true if either:
- \( x = 0 \)
- \( x + 2 = 0 \) → \( x = -2 \)
Thus, there are two solutions: \( x = 0 \) and \( x = -2 \).
Since each of these solutions corresponds to a point where the graph crosses the x-axis, the graph of the function \( f(x) = x(x + 2) \) will cross the x-axis at two points.
Therefore, the graph of \( f(x) = x(x+2) \) crosses the x-axis 2 times.
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