Question

Graph the function f(x)=–3(x+3)^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

Step 1 — identify the vertex and shape
- f(x) = −3(x+3)^2 is in vertex form a(x−h)^2 + k with a = −3, h = −3, k = 0.
- Vertex: (−3, 0).
- Since a = −3 < 0 the parabola opens downward and is vertically stretched by factor 3 (steeper than y = −(x+3)^2).

Step 2 — plot the vertex
- Plot the point (−3, 0).

Step 3 — plot at least one more point (and its symmetric partner)
- Choose x = −2: f(−2) = −3(1)^2 = −3 → point (−2, −3).
- By symmetry, x = −4 gives the same y: (−4, −3).
- You can also plot x = −1: f(−1) = −3(2)^2 = −12 → (−1, −12) to show how steeply it drops.

Step 4 — draw the parabola
- Connect the points with a smooth curve through (−3,0) opening downward, passing through (−2,−3) and (−4,−3), and through (−1,−12) if you plotted it.

Extra useful points/intercepts
- x-intercept: just x = −3 (double root) so the vertex touches the x-axis there.
- y-intercept: f(0) = −27 → (0, −27) (useful if your graphing window is tall enough).

If you make a mistake in an interactive tool
- Select the second point (or the extra point you added) and place it on top of the vertex (−3,0) to remove/overwrite the stray plotted point, then replot the correct second point.