Question

Which of the following functions is equivalent to f(x) = 2( x - 3)2 + 4

-
O f(x) = 2x2 - 6x + 4
O f(x) = 2x2 – 12x + 22
O f(x) = 2x2 + 18x + 4
O f(x) = 2x2 + 12x – 22

Answer 1

`\implies f(x) = 2x^2-12x + 22`

Explanation:

Given :-

• 
  `f(x) = 2(x-3)^2+4`

And we need to find out the function from the given options which is equivalent to the given function . For that firstly simplify the whole square term , that is ,

Using Identity :-

`\implies (a-b)^2= a^2-2ab + b^2`

Whole square term :-

`\implies (x-3)^2= x^2+9-6x`

Now multiply the constant term outside the bracket to it . As ,

`\implies f(x) = (2x^2+18-12x )+ 4`

Add the constant terms .

`\implies f(x) = 2x^2-12x + 22`

Hence the second option is correct .