Question

Graph the function f(x)=2x^2–5.
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 plot f(x) = 2x^2 − 5 by hand (or in a graphing app):

Key facts
- Vertex: (0, −5) (parabola opens upward, axis x = 0).
- y-intercept: (0, −5) (same as vertex here).
- x-intercepts: solve 2x^2 − 5 = 0 → x = ±√(5/2) ≈ ±1.5811.
- Shape: symmetric about the y-axis.

Simple points to plot
- x = 0 → y = −5 → (0, −5) (vertex)
- x = 1 → y = 2(1)^2 − 5 = −3 → (1, −3)
- x = −1 → (−1, −3) (symmetric)
- x = 2 → y = 8 − 5 = 3 → (2, 3)
- x = −2 → (−2, 3)

Suggested plotting range
- x from −3 to 3, y from −6 to 6 to show vertex and a few points.

Steps
1. Draw x- and y-axes and mark a scale.
2. Plot the vertex at (0, −5).
3. Plot another point on the parabola, e.g. (1, −3). You can also plot (−1, −3), (2, 3), (−2, 3).
4. Connect the points with a smooth U-shaped curve symmetric about the y-axis.
5. (If using an app) to erase a mistaken parabola as you described, select the second point and place it exactly on top of the first (so both points coincide) — the app will treat it as removing the second point and you can start again.

That’s all you need to draw f(x) = 2x^2 − 5.