Determine the nature of the roots of the quadratic equation x^2 + 6x + 8 = 0, and plot the graph of this function.

The graph has two distinct real roots (x=-4 and x = -2), which we can see by factorising the equation, which gives (x+4)(x+2) = 0. We can then plot the function y = x^2 + 6x + 8, first marking the roots on the y-axis, then the y-intercept (0,8), and drawing the graph from there.