Question

F(x)=-x²-2x-8 determine the vertex

Answer 1

For a quadratic function like this, the vertices are points of symmetry.
We can use a shortcut such that:
x
=
−
b
2
a

In your case,
b
is 2 and
a
is 1. So:
−
2
2
⋅
1
=
−
1
Answer is -1

Answer 2

vertex = (- 1, - 7 )

Explanation:

Given a parabola in standard form, f(x) = ax² + bx + c (a ≠ 0 )

Then the x- coordinate of the vertex is

`x_(vertex)` = -
`(b)/(2a)`

f(x) = - x² - 2x - 8 ← is in standard form

with a = - 1 and b = - 2, then

`x_(vertex)` = -
`(-2)/(-2)` = - 1

Substitute x = - 1 into f(x) for corresponding y- coordinate

f(- 1) = - (- 1)² - 2(- 1) - 8 = - 1 + 2 - 8 = - 7

vertex = (- 1, - 7 )