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 \( f(x) = 0 \).

Set the equation to zero:

\[
x(x + 2) = 0
\]

This equation can be solved by finding the roots. We can set each factor equal to zero:

1. \( x = 0 \)
2. \( x + 2 = 0 \) which gives \( x = -2 \)

Thus, the solutions are \( x = 0 \) and \( x = -2 \).

Since there are two distinct real roots where the function crosses the x-axis, the graph of \( f(x) = x(x + 2) \) crosses the x-axis **2 times**.

Therefore, the answer is 2 times.