What are the vertex, focus and directrix of y=2x2+11x6?

1 Answer
Dec 19, 2016

The vertex is =(114,1698)
The focus is =(114,1688)
The directrix is y=1708

Explanation:

Let rewrite the equation

y=2x2+11x6

=2(x2+112x)6

=2(x2+112x+12116)61218

y=2(x+114)21698

y+1698=2(x+114)2

12(y+1698)=(x+114)2

This is the equation of the parabola

(xa)2=2p(yb)

The vertex is =(a,b)=(114,1698)

The focus is =(a,b+p2)=(114,1698+18)

=(114,1688)

The directrix is y=bp2

, y=169818=1708

graph{(y-2x^2-11x+6)(y+170/8)=0 [-14.77, 10.54, -21.49, -8.83]}