Find the standard form of the equation of the parabola with the given characteristics and vertex at the origin. Passes through the point (-1, 1/8); vertical axis.

There is no focus of the parabola or equation given, so how am I suppose to solve this problem?

see the other solution I gave.

Same exact problem, just a different point.

V(0,0), P(-1,1/8).

Y = a(x-h)^2 + k.
1/8 = a(-1-0)^2 + 0.
a = 1/8.

Y = 1/8(x-0)^2 + 0.
Y = (1/8)x^2.

To find the standard form of the equation of a parabola, you need either the vertex and the focus or the vertex and one other point on the parabola. In this case, you are given the vertex at the origin (0,0) and a point on the parabola (-1, 1/8). However, the focus of the parabola is not provided.

Unfortunately, without the focus or another specific point, it is not possible to determine the standard form of the equation for this parabola.

If you have any additional information or if there is more context to the problem, please provide that information so that I can assist you further.