Question

Graph the function f(x)=–2x^2+9.
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

Step 1 — find the vertex
- f(x) = −2x^2 + 9 is in form f(x)=ax^2+bx+c with a = −2, b = 0, c = 9.
- Vertex x-coordinate = −b/(2a) = 0, so vertex is at (0, 9). Plot that point.

Step 2 — find and plot additional points (use symmetry)
- x = 1 → f(1) = −2(1)^2 + 9 = 7 → point (1, 7). By symmetry also plot (−1, 7).
- x = 2 → f(2) = −8 + 9 = 1 → points (2, 1) and (−2, 1).
- x-intercepts: solve −2x^2 + 9 = 0 → x = ±3/√2 = ±(3√2)/2 ≈ ±2.121, so approximate intercepts (±2.121, 0).

Step 3 — draw the parabola
- Plot the vertex (0,9) and the symmetric points listed.
- Sketch a smooth U-shaped curve through those points opening downward (since a = −2).

If you need to undo a mistaken parabola in your tool:
- Select the second point you placed and drag it to lie exactly on top of the first point (this will collapse the plotted curve), then re-place the second point where you want it.

Extra notes
- Axis of symmetry: x = 0 (the y-axis).
- Domain: all real x. Range: y ≤ 9.