Question

Graph the function f(x)=–2x^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

Here’s how to graph f(x) = −2x^2 and plot the points requested.

1. Identify the vertex
- Standard form: f(x)=−2x^2 has its vertex at (0,0). Plot (0,0).

2. Pick another point (and its symmetric partner)
- Choose x = 1: f(1) = −2(1)^2 = −2 → point (1, −2). Plot (1, −2).
- By symmetry also plot (−1, −2).
- You can also use x = 2 → f(2) = −8 giving (2, −8) (and (−2, −8)) if you want more shape.

3. Draw the parabola
- Draw a smooth curve through the points (…,−2, −8), (−1, −2), (0,0), (1, −2), (2, −8). The parabola opens downward and is steeper than y = −x^2 because of the factor 2.

4. If you make a mistake in an interactive tool
- You can erase by selecting the second point and placing it on top of the first (or simply delete/move the point), then replot the correct point(s).

Helpful table of values:
- x: −2, −1, 0, 1, 2
- f(x): −8, −2, 0, −2, −8

That will give you an accurate downward-opening parabola with vertex at the origin.