To determine how many times the graph of the function \( f(x) = x(x + 2) \) crosses the x-axis, we need to find the roots of the function. The graph crosses the x-axis where \( f(x) = 0 \).
We can set the equation to zero:
\[ f(x) = x(x + 2) = 0 \]
This product is zero when either factor is zero:
- \( x = 0 \)
- \( x + 2 = 0 \) which simplifies to \( x = -2 \)
Thus, the two solutions (roots) are \( x = 0 \) and \( x = -2 \).
Since we have two distinct roots, the graph of \( f(x) = x(x + 2) \) crosses the x-axis at two points.
Therefore, the graph will cross the x-axis 2 times.