Does the equation y = x2 – 5 have a minimum or maximum value and what is it?

Question

anonymous · Answer

To find a max or min you need to take the first derivative and set it equal to zero. Plug the value you found for X into the second derivative and if it is positive, then it is a min, if it is negative, then it is a max.

directrix · Answer

Look at the variable x^2 in the equation: y = x^2 - 5.
x^2 is never negative for any real value of x. So, the smallest value the expression x^2 + 5 can have is when x itself  produces a minimum value for x^2. That is when x = 0. The minimum value of y would be 5 and that happens when  x = 0. (0,5) Those are also the coordinates of the vertex of the parabola known as y = x^2 - 5 .