What is the vertex of # y=1/2x^2 +2x - 8 #?

1 Answer
Nov 14, 2015

The vertex of a quadratic curve is the point where the slope of the curve is zero.

Explanation:

#y=x^2/2+2x-8#
=> #dy/dx=1/2*2*x+2# (Differentiating both sides with respect to x)
=>#dy/dx=x+2#

Now the slope of the quadratic curve is given by #dy/dx#

Thus, at the vertex ( as mentioned earlier ), #dy/dx=0#

Therefore #x+2=0#
Or #x=-2#

The corresponding y coordinate can be obtained by substituting #x=-2# in the original equation.

#y=x^2/2+2x-8#
=> #y=2^2/2+2*2-8#
=>#y=2+4-8#
=>#y=-2#

This the required vertex is: #(x,y) = (-2,-2)#