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Complete the square, then graph and identify the vertex, focus, directrix, and endpoints of the latus rectum for the equation -14x+2y^2-8y=20
complete the square
divide by 2
This is an equation of a parabola that opens rightwards.
Its standard form: (y-k)^2=4px, (h,k)=(x,y) coordinates of the vertex
For given equation:(y-2)^2=7(x+2)
axis of symmetry: y=2
Focus: (-2+p,2)=(-2+7/4,2)=(-1/4,2) (p distance to the right of the vertex on the axis of symmetry)
Directrix: x=(-2-p)=(-2-7/4)=-15/4 (p distance to the left of the vertex on the axis of symmetry)
length of latus rectum=4p=7
end points: (-1/4,2±2p)
=(-1/4,-1.5) and (-1/4,5.5)
see graph below: