Question

Write f(x) = 2x2 – 44x 185 in vertex form. To write f(x) = 2x2 – 44x 185, factor out from the first two terms. Next, form a perfect square trinomial keeping the value of the function equivalent: f(x) = 2(x2 – 22x 121) 185 – 242 The function written in vertex form is f(x) = (x – )2.

Answer 1

The quadratic function f(x) = 2x² – 44x + 185 is written in vertex form is f(x) = 2(x –  11)² – 57.

What is a quadratic equation?

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

The quadrattic equation is f(x) = 2x² – 44x + 185.

Take common 2 from the equation, we have

$f(x) = 2(x^2 - 22x )+ 185$

Add and subtract 121, we have

$f(x) = 2(x^2 - 22x +121 - 121 )+ 185\\\\f(x) = 2[(x^2 - 11)^2-121]+ 185\\\\f(x) = 2(x-11)^2 - 242 + 185\\\\f (x ) = 2(x-11)^2 -57$

And we know that the standard equation

f(x) = a(x - h)² + k

On comparing, we have

The vertex (h, k) is (11, -57).

More about the quadratic equation link is given below.

brainly.com/question/2263981