Find the value x at which the minimum of the function $f ( x ) = x ^ { 2 } - 2 x + 2$ occurs.
A)1
B) $- \frac { 1 } { 4 }$
C) $- \frac { 1 } { 2 }$
D) $\frac { 3 } { 4 }$
E)0
F) $\frac { 1 } { 4 }$
G)-1
H) $\frac { 1 } { 2 }$

Question

Find the value x at which the minimum of the function $f ( x ) = x ^ { 2 } - 2 x + 2$ occurs.
A)1
B) $- \frac { 1 } { 4 }$ 
C) $- \frac { 1 } { 2 }$
D) $\frac { 3 } { 4 }$  
E)0
F) $\frac { 1 } { 4 }$ 
G)-1
H) $\frac { 1 } { 2 }$

Quizplus · Accepted Answer

The minimum value of the function $f(x) = x^2 - 2x + 2$ occurs at the vertex of the parabola represented by this quadratic equation. The x-coordinate of the vertex can be found using the formula $-\frac{b}{2a}$, where $a = 1$ and $b = -2$ in this case. Plugging these values into the formula gives $-\frac{-2}{2(1)} = 1$, indicating that the minimum occurs at $x = 1$.

Find the Value X at Which the Minimum of the Function