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.

Is the correct formula as follows:

x^2 = 4py

Are these correct steps to take for the above problem???

1. Write original equation.

2. Divide each side by the given number in equation.

3. Write in standard form.

What if there is no focus given for this above problem or a focus of the parabola for an equation? How would I then end up solving this problem? Please help because I am lost and confused.

How do I know which formula to use when it comes to a conic section of the parabola?

For example, I have two separate things listed in my textbook as follows when it comes to the parabola.

Type: Parabola

General Equation: y = a(x-h)^2 + k

Standard Form: (x - h)^2 = 4p (y - k)

Notation:

1. x2 term and y1 term.

2. (h,k) is vertex.

3. (h, k does not equal p) is center of focus, where p = 1/4a.

4. y = k does not equal p is directrix equation, where p = 1/4a.

Value:

1. a > 0, then opens up.

2. a < 0, then opens down.

3. x = h is equation of line of symmetry.

4. Larger (a) = thinner parabola; Smaller (a) = fatter parabola.

Type: Parabola

General Equation: x = a (y-k) ^2 + h

Standard Form: (y - k) ^2 = 4p (x - h)

Notation:

1. x1 term and y2 term.

2. (h,k) is vertex.

3. (h does not equal p, k) is focus, where p = 1/4a.

4. x = h does not equal p is directrix equation, where p = 1/4a.

Values:

1. a > 0, then opens right.

2. a < 0, then opens left.

3. y = k is equation of line of symmetry.

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