Question

Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. Show your work.

f(x) = x2(x + 2)

Answer 1

The x-intercepts will be at x = 0 , -2

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