Respuesta :

calculista

we have

[tex]f(x) = (x-2)^{2}+1[/tex]

This is a quadratic equation (vertical parabola) open up

so

the axis of symmetry is the coordinate x of the vertex

Find the vertex of the function

the vertex is the point---------> [tex](2,1)[/tex]

so

the axis of symmetry is [tex]x=2[/tex]

therefore

the answer in the attached figure

Ver imagen calculista

To solve the problem we must know about the Equation of a parabola.

Equation of a parabola

y = a(x-h)2 + k

where,

(h, k) are the coordinates of the vertex of the parabola in form (x, y);

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

The axis of symmetry for this function is through x=2.

Explanation

Given to us:

  • [tex]f(x) = (x-2)^2 + 1[/tex],

The equation given to us is a quadratic equation which is a vertical parabola and opened on the upside.For this parabola the vertex are (2, 1).

What is symmetry for a parabola?

The axis of symmetry for a parabola is through the coordinate of its vertex. In this case, as the parabola is vertical the axis of symmetry for this parabola is the vertex of x, which is (x=2).

As we can see in the image attached.

Hence, the axis of symmetry for this function is x=2.

Learn more about Quadratic Equation:

https://brainly.com/question/21589886

Ver imagen ap8997154

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