The quadratic function given when converted to vertex form will be: [tex]f(x) = 2(x-11)^2 -57[/tex]
If a quadratic equation is written in the form
[tex]y=a(x-h)^2 + k[/tex]
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
We first take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.
For this case, the given quadratic function is:
[tex]f(x) =2x^2 -44x + 185\\[/tex]
Converting this to the vertex form, we get:
[tex]f(x) =2x^2 -44x + 185\\\\f(x) = 2(x^2 -22x) + 185\\f(x) = 2(x^2 -2 \times 11 \times x + 11^2 - 11^2) + 185\\f(x) = 2((x-11)^2 -121) + 185\\f(x) = 2(x-11)^2 -242 + 185\\f(x) = 2(x-11)^2 -57[/tex]
Thus, the quadratic function given when converted to vertex form will be: [tex]f(x) = 2(x-11)^2 -57[/tex]
Learn more about vertex form of a quadratic equation here:
https://brainly.com/question/9912128
