SOLUTION: write the equation y^2- 8y - 8x = 8 in standard form. Fill in the blanks and sketch the graph. A)vertex: B)Directrix: C)AOS: D)p= E)Latus Rectum= F)focus:

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: write the equation y^2- 8y - 8x = 8 in standard form. Fill in the blanks and sketch the graph. A)vertex: B)Directrix: C)AOS: D)p= E)Latus Rectum= F)focus:      Log On


   

Question 721379: write the equation y^2- 8y - 8x = 8 in standard form. Fill in the blanks and sketch the graph.
A)vertex:
B)Directrix:
C)AOS:
D)p=
E)Latus Rectum=
F)focus:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
write the equation y^2- 8y - 8x = 8 in standard form. Fill in the blanks and sketch the graph.
A)vertex:(-3,4)
B)Directrix:x=-5
C)AOS:y=4
D)p=2
E)Latus Rectum=8
F)focus:(-1,4)
***
y^2-8y-8x=8
complete the square:
(y^2-8y+16)=8x+8+16
(y-4)^2=8x+24
(y-4)^2=8(x+3)
This is an equation of a parabola that opens rightward:
Its basic equation: (y-k)^2=4p(x-h), (h,k)=(x,y) coordinates of the vertex
vertex: (-3,4)
Axis of symmetry: y=4
4p=8
p=2
focus: (-1,4)
directrix: x=-5
latus rectum(focal width)=4p=8
Standard form of equation: (vertex form):
x=(1/8)(y-4)^2-3
see graph below:
y=(8x+24)^.5+4