Question 442284
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Hi
parabola with vertex at (4,-1) and directrix y = 1.
Directrix parallel to the x-axis. Parabola opening upward or downward.
Note: standard form is {{{(x -h)^2 = 4p(y -k)}}}, where  the focus is (h,k + p)
and the directrix is -p distance from the vertex
vertex at (4,-1) directrix y = 1 Parabola opens downward
 (x-4)^2 = -8(y+1)  |directrix y = 1 therefore: p = -2  4p = -8 
or y = (-1/8)(x-4)^2 - 1
{{{drawing(300,300,   -6, 6, -6, 6,  blue(line(4,6,4,-6))  , grid(1),
circle(4, -1,0.3),
circle(4, -3,0.3),
graph( 300, 300, -6, 6, -6, 6,0,1,-(1/8)(x-4)^2 - 1))}}}



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