Question

Graph the function f(x)=–3(x–9)^2–7.
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

Steps to graph f(x) = −3(x − 9)^2 − 7:

1. Find the vertex: the function is in vertex form a(x − h)^2 + k with h = 9, k = −7, so the vertex is (9, −7). Plot that point.

2. Plot another point on the parabola. A simple choice is x = 10:
- f(10) = −3(10 − 9)^2 − 7 = −3(1) − 7 = −10,
so plot (10, −10). (By symmetry (8, −10) is also on the curve.)

3. Sketch the parabola:
- It opens downward because a = −3 < 0.
- It is relatively narrow (|a| = 3).
- Use the vertex (9, −7) and the plotted point(s) to draw a smooth symmetric downward curve with axis of symmetry x = 9.

Notes:
- If you need more accuracy, plot (11, −19) and (7, −19) since f(11) = f(7) = −3(2)^2 −7 = −19.
- There are no real x-intercepts (the parabola never crosses the x-axis); the y-intercept is f(0) = −250 (far below), so don’t rely on it for a neat sketch.
- To erase and start over as you mentioned: select the second point and place it on top of the vertex to remove the sketched parabola, then place a new second point.