Final answer:
To graph the function f(x) = (x+2)(x-4), find the vertex of the parabola using the formula h = -b/(2a) and plot it at (1, -3). Then choose another point, like (0, -8), to help with the shape of the graph. Connect these with a smooth U-shaped curve to represent the parabola.
Step-by-step explanation:
To graph f(x) = (x+2)(x-4), you are essentially plotting a parabola, which is a U-shaped graph. This function can be expanded to f(x) = x2 - 2x - 8. To find the vertex of the parabola, we use the fact that for a quadratic equation in the form y = ax2 + bx + c, the vertex (h,k) can be found using h = -b/(2a). For our equation, a = 1 and b = -2, giving us the vertex at h = -(-2)/(2*1) = 1. Substituting x = 1 back into the equation gives us the y-coordinate of the vertex: f(1) = (1+2)(1-4) = -3, so the vertex is at (1, -3).
Then we choose another point on the parabola to help complete the graph. Let's choose x = 0. Substitute x = 0 into the equation to get f(0) = (0+2)(0-4) = -8. Therefore, the point (0, -8) is on the parabola.
Using graphing tools, you often have features that facilitate plotting such equations such as a parabola tool which would make this process easier. However, for manual plotting, plotting the vertex and additional points and then drawing a smooth curve that fits these points would give you the representation of the parabola for f(x).