What Point on the Surface Z Is Closest to the Origin

What point on the surface z is closest to the origin $z = x ^ { 2 } + y - 5$
Hint : Minimize the square of the distance from $( x , y , z )$ to the origin.

A) $( 2.5,0 , - 2.5 )$
B) $\left( - 2 , \frac { 1 } { 2 } , - \frac { 1 } { 2 } \right)$ and $\left( 2 , \frac { 1 } { 2 } , - \frac { 1 } { 2 } \right)$
C) $( 0,2.5 , - 2.5 )$
D) $\left( 0 , \frac { 1 } { 2 } , - \frac { 1 } { 2 } \right)$
E) $( 0,2.5 , - 2.5 )$ and $( 0,2.5,2.5 )$

Correct Answer:

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