What are the vertex and x-intercepts of the graph of the function given below?
y=x² - 2x - 24

The answer to your question is Vertex (1, - 25)  

                                                     x-intercepts = -4, 6

Step-by-step explanation:

Data

Function   y = x² - 2x - 24

Vertex = ?

x- intercepts = ?

Process

1.- Factor to find the vertex

                  y = x² - 2x - 24

                  y + 24 = x² - 2x

                  y + 24 + (1)² =   x² - 2x + (1)²

                  y + 24 + 1 = x² - 2x + 1

                  y + 25 = (x - 1)²

Vertex = (1, -25)

2.- See the graph below

From the graph, we get the x-intercepts

          x₁ = -4    x₂ = 6