How many times will the graph of f(x)=x(x+2)
cross the x-axis?
To determine how many times the graph of f(x)=x(x+2) crosses the x-axis, we need to find the number of x-intercepts.
An x-intercept occurs when the y-coordinate (or the value of f(x)) is equal to zero.
Setting f(x) = 0, we have:
0 = x(x+2)
Using the zero product property, we can set each factor equal to zero:
x = 0 or x+2 = 0
For x = 0, the value of f(x) is 0 since anything multiplied by 0 is 0.
For x+2 = 0, we subtract 2 from both sides to isolate x:
x = -2
Therefore, the graph of f(x)=x(x+2) crosses the x-axis twice: once at x=0 and once at x=-2.
To find the number of times the graph of the function f(x) = x(x+2) crosses the x-axis, we need to determine the number of distinct x-values where f(x) = 0.
Setting f(x) = 0, we have:
x(x + 2) = 0
Since the product of two numbers is zero if and only if at least one of the numbers is zero, we get two possibilities:
1. x = 0
2. x + 2 = 0 => x = -2
Therefore, the graph of f(x) = x(x+2) crosses the x-axis at two distinct points: x = 0 and x = -2.