Parabola help (Locus) (1 Viewer)

[j1mmy_]

Need help to find the equation of the directrix and the coordinates of the focus.

(a) Sketch y= x²+2x-8, showing intercepts and the minimum point.
(b) Find the coordinates of the focus and the equation of the directrix of the parabola.

Part a done, giving (-1, -9) as the minimum which is also the vertex.

Part b, I'm lost.

 

[Carrotsticks]

For part (b), you have to complete the square to put it in the familiar form (x-h)^2 = 4a (y-k), then you can proceed to find the focus and directrix as usual.

 

[j1mmy_]

For part (b), you have to complete the square to put it in the familiar form (x-h)^2 = 4a (y-k), then you can proceed to find the focus and directrix as usual.

Thanks that helps!

By the way, how would I approach this question:
Find the equation of the parabola with vertex (-2, 3) that also passes through (2, 1) and is concave downwards.

 

[Carrotsticks]

Since it is concave downwards and has vertex (-2,3), it has the general form -(x+2)^2 = 4a (y-3)

To find 'a', simply substitute x=2, y=1, then solve for 'a'.