Question

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

Answer 1

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)`