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

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

solve the equation by factoring.

c^2-4c=0

Part A) The vertex is the point

Part B) The axis of symmetry is

Part C)

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

Part 2) Solve the equation by factoring.

we have

Factor c

so

and

------->

The solutions are

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step-by-step explanation: