Need help and will be giving Brainliest

x-intercept (s):

For this case h (x) = 0

x2 - 2x - 8 = 0

(x-4) * (x + 2) = 0

x1 = 4

x2 = -2

y-intercept:

For this case x = 0

h (0) = (0)2 - 2 (0) - 8

h (0) = - 8

vertex:

We derive the equation:

h '(x) = x2 - 2x - 8

h (x) = 2x - 2

We match zero:

2x-2 = 0

x = 2/2

x = 1

We evaluate the function for x = 1

h (1) = (1)2 - 2 (1) - 8

h (1) = 1 - 2 - 8

h (1) = -9

The vertex is:

(1, -9)

axis of symmetry of the function:

x = 1

Step-by-step explanation:

hope it helps