Final answer:
To graph f(x) = (x + 3)(2x + 1), practice plotting points on a coordinate plane, use graphing technology, and understand quadratic functions. The answer is D. All of the above, as each method contributes to understanding the graph.
Step-by-step explanation:
To learn to graph the function f(x) = (x + 3)(2x + 1), it is helpful to:
- Practice plotting points on the coordinate plane to understand the shape of the graph.
- Use a graphing calculator or software to visualize the graph, which can handle the tedious work of plotting many points accurately.
- Understand the behavior of quadratic and linear functions, since this function is a quadratic, and knowing its general shape (a parabola) can guide you in graphing it.
So, the answer to the question would be D. All of the above.
Additionally, when graphing the function by hand, consider the following steps:
- Find the x-intercepts by setting the function equal to zero and solving for x.
- Find the vertex by using the formula for the x-coordinate of the vertex of a parabola, x = -b/(2a), where a and b are the coefficients from the standard form ax^2 + bx + c.
- Plot the x-intercepts, the vertex, and a few additional points to give the shape of the parabola.
- Draw a smooth curve through the points.