Solve the quadratic by factoring
identify the x-intercepts, y-intercept, and vertex & explain

x-intercepts are (3,0) and (-2, 0).

The y-intercept  is (0, -6).

Vertex is (0.5, -6.25).

Step-by-step explanation:

6 = x^2 - x

x^2 - x - 6 = 0

(x - 3)(x + 2) = 0

x = 3, -2 so the x-intercepts are (3, 0) and (-2, 0).

The y-intercept occurs when x = 0, so

y = (0)^2 - (0) - 6 = -6.

The y-intercept  is (0, -6).

The  coordinate of the vertex  is -b/2a = -(-1) / 2 = 0.5.

When x = 0.5,  f(x) = (0.5)^2 - 0.5 - 6 = -6.25.

So the vertex is at (0.5, -6.25).