Question

Choose the correct vertex of the function f(x) = x2 - x + 2.

Answer 1

Rewrite it into vertex form with completing the square:
f(x) = x^2 - x + 2 = (x^2 - x) + 2 = (x^2 - x + 1/4) + 2 + 1/4 = (x - 1/2)^2 + 9/4;

So the vertex is (1/2, 9/4).

Answer 2

Vertex is
`((1)/(2), (7)/(4))`

Explanation:

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

To find out vertex we use formula

`x= (-b)/(2a)`

From the given f9x), a= 1 and b = -1

Plug in the values in the formula

`x= (-(-1))/(2(1))=(1)/(2)`

Now plug in 1/2 for x in f(x)

`f((1)/(2))= ( (1)/(2))^2 - ((1)/(2))+2=(7)/(4)`

So vertex is (1/2 , 7/4)