Graphically

Finding Solutions

Example 2

What are the zeros of this polynomial function, P(x) = -x4 - 3x3 + 6x2 + 8x?

PolyGraphEx2-1

Step 1. Estimate the x-intercepts of the graph.

It appears that the zeros of the function are x = -4, x = -1, x = 0, and x = 2.

Step 2. Check the estimates by substituting into the equation.

PolyGraphEx2-2

Because the point is (-4, 0), x = -4 is an x-intercept, or zero, of the equation.

Check the remaining values to ensure accuracy.

PolyGraphEx2-3b

The zeros of the function are x = -4, x = -1, x = 0, and x = 2.