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Find the vertex and write the quadratic function in vertex form (which our OpenStax textbook also calls the standard form).f(x)=x2−12 x + 117

Find the vertex and write the quadratic function in vertex form which our OpenStax textbook also calls the standard formfxx212 x 117 class=

Respuesta :

Given

[tex]f(x)=x^2-12x+117[/tex]

To find:

The vertex and the equation in vertex form.

Explanation:

It is given that,

[tex]f(x)=x^2-12x+117[/tex]

That implies,

[tex]\begin{gathered} f(x)=x^2-12x+117 \\ f(x)=[(x-6)^2-36]+117 \\ f(x)=(x-6)^2+81 \\ y-81=(x-6)^2 \end{gathered}[/tex]

Hence, the vertex is (6,81) and the vertex form of the equation is

[tex]y=(x-6)^2+81[/tex]

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