SOLUTION: Identify the coordinates fo the vertex and focus, the equations of the axis of symmetry and directrix and the direction of opening of the parabola with equation y= -2x^2-16x-27

Question 750691: Identify the coordinates fo the vertex and focus, the equations of the axis of symmetry and directrix and the direction of opening of the parabola with equation
y= -2x^2-16x-27
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Identify the coordinates fo the vertex and focus, the equations of the axis of symmetry and directrix and the direction of opening of the parabola with equation
y= -2x^2-16x-27
complete the square:
y=-2(x^2+8x+16)+32-27
y=-2(x+4)^2+5
parabola opens downward:
vertex: (-4,5)
axis of symmetry: x=-4
standard (vertex) form of equation: , (h,k)=(x,y) coordinates of the vertex
basic form of equation:
y=-2(x+4)^2+5
-2(x+4)^2=(y-5)
(x+4)^2=-(1/2)(y-5)
4p=1/2
p=1/8
focus:(-4,39/8) (p-distance below vertex on the axis of symmetry)
directrix: y=41/8 (p-distance above vertex on the axis of symmetry)
see graph below as a visual check:

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