Question

Graph the function f(x)=–3x^2.
Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

Answer 1

f(x) = −3x^2 is a downward-opening parabola with vertex at the origin.

Steps to plot:
1. Vertex: plot (0, 0). This is the maximum.
2. Choose another point on the parabola, e.g. x = 1 → f(1) = −3(1)^2 = −3, so plot (1, −3). By symmetry also plot (−1, −3).
3. (Optional) Add a farther point for shape: x = 2 → f(2) = −12, so (2, −12) and (−2, −12).
4. Draw a smooth curve through the points; the axis of symmetry is the y-axis (x = 0). The parabola opens downward and is steeper than y = −x^2 because of the factor 3.

If you need to erase and start over, place the second plotted point directly on top of the vertex (the first point) — that will collapse the parabola.