Question

What is the equation of a parabola with a vertex at(-2,0) and a directrix x=-4

Answer 1

since the directrix is a vertical line, the parabola be like a sideways "u"
vertex form for a sideways parabola is: 4p(x – h) = (y – k)^2
let's plug in what we know: 4p(x - 2) = (y - 0)^2 now, we'll find p
the distance (p) between the vertex and the directrix is absolute value( (directrix) - k)
so with the real numbers it'll be absolute value( (-4) - (2) )
simplify this, and we get: absolute value( (-6) )
the parabola points to the right, so p= 6
so let's plug in 6 for p
and we get: 4(6)(x - 2) = (y)^2
this simplifies to 24(x - 2) = y^2
you can leave it like this, or distribute the 24, to get: 24x - 48 = y^2
Hope this was helpful