Question

How many times will the graph of f(x)=x(x+2)
cross the x-axis?(1 point)
time(s)

Answer 1

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:

1. \( x = 0 \)
2. \( x + 2 = 0 \) → \( x = -2 \)

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**.