Draw the line of y = (y - 2)² , x >= 2

Answer 1

To draw the line y = (y - 2)², we need to understand the equation first.

The equation y = (y - 2)² represents a vertical parabola. When we expand the squared term, we get y = y² - 4y + 4. Rearranging the equation, we have y² - 5y + 4 = 0.

To find the x-intercepts, we set y equal to 0 and solve for x:
0 = x² - 5x + 4
0 = (x - 1)(x - 4)

So the x-intercepts are x = 1 and x = 4.

Now let's plot the graph:

- First, mark the x-intercepts: (1, 0) and (4, 0).
- Next, find the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = 1 and b = -5. Plugging in these values, we have x = -(-5)/(2*1) = 5/2 = 2.5. Therefore, the vertex is (2.5, 2.25).
- Since x ≥ 2, we only need to plot the part of the parabola to the right of x = 2.
- As x increases, y also increases according to the equation y = (y - 2)².

Here's the corresponding graph:

|
|
| .
| .
-------------------+--------------->
(1,0) | x-axis
(2.5,2.25) | (vertex)
(4,0) |

Please note that the graph is not accurately to scale and is meant to provide a visual representation of the parabola.