parabola equation from vertex and focus

Question

How do you create a parabola equation from a vertex of (1,5) and a focus of (1,-9)?

Answer 1

Try using this form:

(x - h)²=4p(y - k)

Vertex is (h, k)

Your vertex is (1, 5), so h = 1 and k = 5

 

Focus is (h, k+p).

Your focus is (1, -9) which means k + p = -9.

We know k = 5, so 5 + p = -9, which means p = -14.

 

Now just plug in all the numbers:

(x - 1)²=4(-14)(y - 5)

Answer 2

vertex (x, y) is (-b/2a, (4ac - b²)/4a)

focus (x, y) is (-b/2a, (1 + 4ac - b²)/4a)

final equation: y = ax² +bx + c