Answer:
<h2>YES. These points are collinear.</h2>
Step-by-step explanation:
If three points are collinear, then the slopes are the same.
The formula of a slope:

For (0, -10) and (-3, -13):

For (-3, -13) and (2, -8):

We can check the last pair (0, -10) and (2, -8):

To write the given quadratic equation to its vertex form, we first form a perfect square.
x² - 2x + 5 = 0
Transpose the constant to other side of the equation,
x² - 2x = -5
Complete the square in the left side of the equation,
x² - 2x + (-2/1(2))² = -5 + (-2/1(2))²
Performed the operation,
x² - 2x + 1 = -5 + 1
Factor the left side of the equation,
(x - 1)² = -4
Thus, the vertex form of the equation is,
<em> (x-1)² + 4 = 0</em>