How many times will the graph of f(x)=x(x+2) cross the x-axis?(1 point)
The graph of f(x)=x(x+2) will cross the x-axis at different points where the y-coordinate is equal to zero. To find these points, we set f(x) equal to zero and solve for x:
x(x+2) = 0
This equation will be true if either x=0 or x+2=0. Solving these two equations gives us:
For x=0:
0(0+2) = 0
For x+2=0, we subtract 2 from both sides to get:
x = -2
So, the graph of f(x)=x(x+2) will cross the x-axis at two points, x=0 and x=-2.
To determine the number of times the graph of the function f(x) = x(x + 2) crosses the x-axis, we need to find the number of real roots of the function.
To find the real roots, we set f(x) equal to zero:
0 = x(x + 2)
Next, we can use the zero product property, which states that if a product of two factors is equal to zero, then at least one of the factors must be zero.
So, we have two cases to consider:
Case 1: x = 0
If x = 0, then the first factor is zero, and the equation becomes:
0 = 0(x + 2)
0 = 0
Case 2: x + 2 = 0
If x + 2 = 0, then the second factor is zero, and the equation becomes:
0 = x(0 + 2)
0 = 2x
Solving each case individually, we find that x = 0 in Case 1 and x = 0 in Case 2.
Therefore, the graph of the function f(x) = x(x + 2) crosses the x-axis at two distinct points: x = 0 and x = -2.
So, the graph of the function crosses the x-axis twice.
To determine how many times the graph of the function f(x) = x(x + 2) crosses the x-axis, we need to consider the roots or x-intercepts of the function. A function crosses the x-axis when its y-value (or output) is equal to zero.
To find the x-intercepts, we set f(x) = 0:
x(x + 2) = 0
Using the zero product property, we know that either x = 0 or (x + 2) = 0.
For x = 0, the equation becomes:
0(0 + 2) = 0
This is true, and we have found one root.
For (x + 2) = 0, we solve for x:
x + 2 = 0
x = -2
So, we have two roots: x = 0 and x = -2.
Thus, the graph of f(x) = x(x + 2) crosses the x-axis two times.