Question

The turning point of the curve: y=6-4x-x^2​

Answer 1

The turning point is (-2,10)

Explanation:

we have

`y=6-4x-x^(2)`

This is a quadratic equation (vertical parabola) open downward

we know that

The turning point of a quadratic equation is the vertex

so

Convert the quadratic equation into vertex form

`y-6=-4x-x^(2)`

`y-6=-(x^(2)+4x)`

`y-6-4=-(x^(2)+4x+4)`

`y-10=-(x^(2)+4x+4)`

`y-10=-(x+2)^(2)`

`y=-(x+2)^(2)+10` ----> equation in vertex form

The vertex is the point (-2,10)

therefore

The turning point is (-2,10)