Question

Graph the function f(x)=4(x–9)^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

Step 1 — find the vertex
- f(x) = 4(x − 9)^2 − 5 is in vertex form y = a(x − h)^2 + k, so the vertex is (h,k) = (9, −5). Plot the point (9, −5).

Step 2 — pick and plot another point
- Choose x = 10: f(10) = 4(10 − 9)^2 − 5 = 4(1)^2 − 5 = −1, so plot (10, −1).
- By symmetry also (8, −1) is on the parabola because (8 − 9)^2 = (10 − 9)^2.

Optional extra points to make the shape clear:
- x = 11: f(11) = 4(2)^2 − 5 = 16 − 5 = 11 → (11, 11)
- x = 7: f(7) = 4(−2)^2 − 5 = 11 → (7, 11)

Step 3 — draw the parabola
- Draw a smooth U-shaped curve opening upward through the plotted points. The axis of symmetry is the vertical line x = 9.

Erasing a mistake
- If you need to remove the parabola in your graphing tool, select the second point you used to create the parabola and place it on top of the vertex (i.e., move it to (9, −5)); that will erase the parabola per the tool’s instructions.