What is the vertex of y=1/2x^2 +2x - 8 y=12x2+2x8?

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-8y=x22+2x8
=> dy/dx=1/2*2*x+2dydx=122x+2 (Differentiating both sides with respect to x)
=>dy/dx=x+2dydx=x+2

Now the slope of the quadratic curve is given by dy/dxdydx

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

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

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

y=x^2/2+2x-8y=x22+2x8
=> y=2^2/2+2*2-8y=222+228
=>y=2+4-8y=2+48
=>y=-2y=2

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