Answer:
The x-intercepts will be at x = 0 , -2
Step-by-step explanation:
Given
f(x) = x²(x+2)
To find the x-intercepts ⇒ f(x) = 0
∴ x²(x+2) = 0
∴ x² = 0 OR x+ 2 = 0
∴ x = 0 or x = -2
So, the x-intercepts will be at x = 0 , -2
To figure out whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept, we need to graph the function f(x)
The attached figure represents the graph of f(x)
As shown in the figure:
1) The graph crosses the x-axis at x = -2
2) The graph touches the x-axis and turns around at x = 0
