Question

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

Answer 1

For equation:

`f(x)=x^2-16x+55`

Vertex:
`(8,-9)`

Axis of symmetry, (
`x=8`)

For equation,

`f(x)=x^2-16+55`

Vertex:
`(0,39)`

Axis of symmetry, (
`x=0`)

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,

`f(x)=x^2-16x+55`

Group,

`=(x^2-16x)+55`

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

`=(x^2-16x+64)+55-64`

Simplify,

`=(x-8)^2-9`

Vertex:
`(8,-9)`

Axis of symmetry, (
`x=8`)

Possibility 2

If the given equation is the following,

`f(x)=x^2-16+55`

Combine like terms,

`=x^2+39`

Put in vertex form,

`=(x)^2+39`

Vertex:
`(0,39)`

Axis of symmetry, (
`x=0`)

Answer 2

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:

• I have graphed the equation on a program. When graphed, the the lowest point lies on the point (0, 39).

• This makes (0, 39) the vertex.

⸻⸻⸻⸻

• The axis of symmetry is a vertical line that intercepts the vertex.
• The vertical line makes the parabola seem 'symmetrical'.
• The 'x' value of the vertex is usually the line of symmetry as well.

⸻⸻⸻⸻

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

⸻⸻⸻⸻

See the graph that I have attached.

⸻⸻⸻⸻

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