Answer and Step-by-step explanation:
To graph the function f(x) = -(x - 6)^2 using the vertex and axis of symmetry, follow these steps:
Step 1: Find the vertex and axis of symmetry.
The given function is in vertex form, which is y = a(x - h)^2 + k. The vertex of the parabola is the point (h, k), and the axis of symmetry is the vertical line x = h.
In this case, a = -1, h = 6, and k = 0. The vertex is (6, 0), and the axis of symmetry is x = 6.
Step 2: Plot the vertex and draw the axis of symmetry.
On the graph, plot the point (6, 0) as the vertex. Then, draw a dashed vertical line at x = 6 to represent the axis of symmetry.
Step 3: Plot other points and draw the graph.
To draw the graph, you can choose some x-values on both sides of the axis of symmetry and calculate the corresponding y-values using the function f(x) = -(x - 6)^2.
For example:
- When x = 4, f(4) = -(4 - 6)^2 = -(-2)^2 = -4
- When x = 5, f(5) = -(5 - 6)^2 = -(-1)^2 = -1
- When x = 7, f(7) = -(7 - 6)^2 = -(1)^2 = -1
- When x = 8, f(8) = -(8 - 6)^2 = -(2)^2 = -4
Now, plot these points (4, -4), (5, -1), (7, -1), and (8, -4) on the graph.
Step 4: Draw the parabola.
Finally, draw a smooth curve through the plotted points to represent the graph of the function. I recommend using graphing software or online graphing tools to plot the function using the given information. Simply input the function f(x) = -(x - 6)^2 and draw the dashed line x = 6 for the axis of symmetry. The graph should show a downward-opening parabola with the vertex at (6, 0) and the axis of symmetry as a vertical line passing through x = 6.