or A parabola opening up or down has vertex (0,0) and passes through ( – 4, – 4). Write its equation in vertex form.

Answer 1

parabola with vertex at the origin, passing through the point (-4,-4)

is

y = ax^2

-4 = a(-4)^2 = 16a

a = -4/16 =- 1/4

y = -(x^2)/4 is the parabola's equation

or more explicitly in vertex form, y=a(x-h)^2 + k with (h,k) = (0,0) = vertex

y = (-1/4)(x-0)^2 + 0^2

but that collapses to

y = -(x^2)/4

it's a downward opening parabola

passing through (-4,-4) with vertex (0,0)

and passing through a symmetric point (4,-4), symmetric about the y axis

it may help to sketch the parabola and points

line of symmetry is the y axis or the line x=0