SOLUTION: ``Find the vertex, focus, directrix, and axis of symmetry of each parabola. x^2+8y+4x-4=0 We have been using the formulas y-k=a(x-h)^2 and x-h=a(y-k)^2 I don't understand whic

Question 193559This question is from textbook algebra and trigonometry structure and method book 2
: ``Find the vertex, focus, directrix, and axis of symmetry of each parabola.
x^2+8y+4x-4=0
We have been using the formulas y-k=a(x-h)^2 and x-h=a(y-k)^2 I don't understand
which to use here, even after completing the square and its confusing because I
don't know which is which. please explain and be specific. thank you. We also
use the fact that the focus is F(h,k+c) when a=1/4c. Please explain in these
terms so that I can understand. thank you This question is from textbook algebra and trigonometry structure and method book 2

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the vertex, focus, directrix, and axis of symmetry of each parabola.
x^2+8y+4x-4=0
We have been using the formulas y-k=a(x-h)^2 and x-h=a(y-k)^2 I don't understand which to use here, even after completing the square and its confusing because I don't know which is which. please explain and be specific. thank you. We also use the fact that the focus is F(h,k+c) when a=1/4c. Please explain in these terms so that I can understand. thank you
-------------
x^2+8y+4x-4=0
-----------------
Complete the square on the x-terms
x^2 + 4x + ? = -8y+4 + ?
x^2 + 4x + 4 = -8y + 4+4
(x+2)^2 = -8(y-1)
------------------------
Rearrange:
(x-1) = (-1/8)(y+2)^2
h = 1, k= -2, a = -1/8 = (1/4)c
c = -1/2
----------------------
Find the vertex, focus, directrix, and axis of symmetry of each parabola.
Vertex = (h,k) = (1,-2)
Focus = (h+c, k) because this parabola is opening to the left.
Focus = (1-(1/2),-2) = ((1/2),-2)
Directrix: x = h - c = 1+1/2 = 3/2
Axis of symmetry: Horizontal line passing thru the vertex:
y = -2
=================================================================
Cheers,
Stan H.
RELATED QUESTIONS
Find the vertex, focus, directrix, and axis of symmetry of each parabola. x^2+8y+4x-4=0 (answered by jim_thompson5910)

Find the vertex, focus, directrix, and axis of symmetry of each parabola. x^2+8y+4x-4=0 (answered by Mathtut,jim_thompson5910)

Find the vertex, focus, directrix, and axis of symmetry of each parabola. x^2+8y+4x-4=0 (answered by jim_thompson5910)

Find the vertex, focus, directrix, and axis of symmetry of each parabola. We have... (answered by solver91311)

I need to find the vertex, focus, directrix and axis of symmetry of the parabola:... (answered by lynnlo)

find the properties of parabola: y^2=x vertex: axis of symmetry focus directrix... (answered by josgarithmetic)

How do you find the vertex, focus, directrix, and axis of symmetry of the parabola?... (answered by ewatrrr,lwsshak3,John10)

find the properties of parabola: x^2-y=0 vertex: axis of symmetry focus directrix... (answered by stanbon)

name the direction vertex Axis of symmetry focus directrix of the parabola y= -1/4x^2 (answered by lwsshak3)