Plot the y-intercept at (0, 4) and zeros at (-2, 0), (1, 0), and (2, 0). Connect these points with a smooth curve, depicting the cubic behavior of G(x) = x^3 - x^2 - 4x + 4.
To graph the polynomial function G(x) = x^3 - x^2 - 4x + 4, follow these steps:
1. Identify Key Points:
- Y-intercept: The y-intercept is the point where the graph crosses the y-axis. For G(x), the y-intercept is (0, 4).
- Zeros/Roots: The zeros are the x-values where G(x) equals zero. The zeros for G(x) are x = -2, x = 1, and x = 2.
2. Plot Key Points:
- Plot the y-intercept at (0, 4).
- Mark the zeros at (-2, 0), (1, 0), and (2, 0).
3. Determine Behavior:
- As x approaches negative infinity, G(x) goes to negative infinity.
- As x approaches positive infinity, G(x) goes to positive infinity.
4. Sketch the Curve:
- Connect the plotted points with a smooth curve, taking into account the behavior described above.
Your graph should exhibit the characteristic behavior of a cubic polynomial, crossing the x-axis at the zeros and intersecting the y-axis at the y-intercept.