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

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.