Identify the axis of symmetry and vertex of f(x) = –x^ 2 –2x–1.

axis of symmetry: x = – 1; vertex: ( 1, 0)
axis of symmetry: x = 1; vertex: (1, 0)
axis of symmetry: x = – 1; vertex: (– 1, 0)
axis of symmetry: x = 1; vertex: (– 1, –1)

Part A) The vertex is the point

Part B) The axis of symmetry is

Step-by-step explanation:

Part 1)

we know that

The equation of a vertical parabola into vertex form is equal to

where

(h,k) is the vertex of the parabola

and the axis of symmetry is equal to the x-coordinate of the vertex

so

-----> equation of the axis of symmetry

In this problem we have    

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

-----> equation in vertex form

The vertex of the parabola is the point

Is a vertical parabola open downward

The axis of symmetry is equal to

see the attached figure to better understand the problem

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation:

if x = 1, then the answer is 3.5