Question

Identify the vertex focus and directrix of the graph x^2-8x-28y-124=0
a. vertex (4,5) focus (4,2) directrix y=2.
b.vertex(-4,5) focus (0,7) directrix y=7
c.vertex (4,-5) focus (4,2) directrix y=-12
d.vertex (-4,5) focus (4,-12) directrix y=2

Answer 1

this is \[x^2 - 8x + 16 = 28y + 140\]

or \[(x -4)^2 = 28(y + 5)\]

\[ (x^-4)^2 = 4 \times 7 (y +5)\]

the equation is now in the form \[(x+h)^2 = 4a(y+k)\]

the parabola is concave up


h = 4, k = -5, a = 7
vertex is at (h, k)

focus is (h, k + a)

directrix is y = k - a