A parabola can be drawn given a focus of (-4, 4) and a directrix of y = –6. Write the equation of the parabola in any form.
+130515 The directrx is below the focus.....so this parabola turns upward
p = the distance between the focus and directrix / 2 = (4 - - 6) / 2 = 10 /2 = 5
So the vertex = ( - 4, 4 - p) = ( -4, 4 -5) = (-4, -1)
So we have this form
4p ( y - k) = (x - h)^2 where (h, k) is the vertex.......so....we have
4(5) ( y - -1) = ( x + 4)^2 simplify
20 (y + 1) = ( x + 4)^2
20y + 20 = x^2 + 8x + 16 subtract 20 from both sides
20y = x^2 + 8x - 4 divide both sides by 20
y = (1/20)x^2 + (2/5)x - (1/5)
Here's the graph : https://www.desmos.com/calculator/5tzekvcuhj
