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How do I change the parabola equation (x-0)^2=4p(y-10) from vertex form to standard form?

User Sabeeh
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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.
User PeaceFrog
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