Find the axis of symmetry and the vertex of the graph of f (x) = x^2 - 16 + 55

Hi there!  

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I believe your answer is:  

Vertex: (0, 39)

Axis of Symmetry: x = 0  

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Here’s why:

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The 'x' value of the vertex is '0', so the axis of symmetry is .

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See the graph that I have attached.

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Hope this helps you. I apologize if it’s incorrect.  

For equation:

Vertex:

Axis of symmetry, ()

For equation,

Vertex:

Axis of symmetry, ()

Step-by-step explanation:

The x-coordinate of the vertex of a parabola indicates the line of symmetry of the parabola. Thus, to solve this problem, one must find the vertex of the parabola. This can be done through a process called completing the square.

Completing the square is a process that converts a quadratic equation in standard form into vertex form. The first step is to group the linear and quadratic terms. Then factor out the coefficient of the quadratic term. After doing so, add a term to make the group a perfect square trinomial, then balance the equation.

Possibility 1

If the given equation is the following,

Group,

There is no quadratic term, thus, complete the square,

Simplify,

Vertex:

Axis of symmetry, ()

Possibility 2

If the given equation is the following,

Combine like terms,

Put in vertex form,

Vertex:

Axis of symmetry, ()

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be