Respuesta :

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:

Vertex is [tex](\frac{1}{2}, \frac{7}{4})[/tex]

Step-by-step explanation:

[tex]f(x) = x^2 - x + 2[/tex]

To find out vertex we use formula

[tex]x= \frac{-b}{2a}[/tex]

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

Plug in the values in the formula

[tex]x= \frac{-(-1)}{2(1)}=\frac{1}{2}[/tex]

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

[tex]f(\frac{1}{2})= ( \frac{1}{2})^2 - (\frac{1}{2})+2=\frac{7}{4}[/tex]

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