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 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:

1. \( x = 0 \)
2. \( x + 2 = 0 \) 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**.