Question

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

Answer 1

Given

`f(x)=x^2-12x+117`

To find:

The vertex and the equation in vertex form.

Step-by-step explanation:

It is given that,

`f(x)=x^2-12x+117`

That implies,

`\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}`

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

`y=(x-6)^2+81`