Question

What is the extreme of the following function
$y = - x^{2} + 2$

Answer 1

It is a quadratic function with graph as parabola

and its maximum lies at the vertex

So we have to find the vertex

So firstly compare it with y=ax^2 +bx +c

we get a=-1 and b=0 and c=2

So to find the vertex (h,k)

$h=\frac{-b}{2a}= \frac{-0}{2(-1)}= 0$

to find k , plug h=0 inplace of x in the function

$h=-(0)^2 +2 = 2$

So vertex is (0,2)

And the maximum value is (0,2) which is the extreme of the function