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

Algebra ->  Quadratic-relations-and-conic-sections -> 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      Log On


   

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) About Me  (Show Source):
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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: y=A%28x-h%29%5E2%2Bk, (h,k)=(x,y) coordinates of the vertex
basic form of equation: %28x-h%29%5E2=-4p%28y-k%29
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:
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%5E2-16x-27%29+