The vertex form of a parabola is:
(x - h)^2 = 4p(y - k)
where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus.
To convert the given equation (x - 0)^2 = 4p(y - 10) from vertex form to standard form, we can follow these steps:
1. Rewrite the equation using the standard form constant, "a":
(x - h)^2 = 4a(y - k)
In this case, h = 0, so we have:
x^2 = 4a(y - 10)
2. Divide both sides of the equation by 4a:
x^2 / 4a = y - 10
3. Add 10 to both sides of the equation:
x^2 / 4a + 10 = y
4. Multiply both sides of the equation by 4a:
x^2 + 40a = 4ay
5. Rearrange the terms so that the equation is in standard form, with the highest power of x first:
4ay = x^2 + 40a
6. Divide both sides of the equation by 4a:
y = (1/4a)x^2 + 10
Therefore, the standard form of the parabola equation (x-0)^2=4p(y-10) is y = (1/4p)x^2 + 10.