what is the value of \( x \) where \( x^2 – x + 3 \) is a minimum?

what is the value of \( x \) where \( x^2 – x + 3 \) is a minimum?

=> \( x^2 – x + 3 \)

If a is positive ( a>0 ), the vertex is a MINIMUM.

If a is negative ( a<0 ), the vertex is a MAXIMUM.

a= 1, b= -1, and c =3

Since a is positive, the vertex is a MINIMUM.

X value of the minimum vertex:

\( x = {-b \over 2a} \)

\( x = {- (-1)  \over 2} \)

\( x = {1  \over 2} \)

\( x = 0.5 \)