Using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created?

Solution:

It is given that

Directrix y = 5

Focus = (4, 1)

We know that a vertex is half of the distance between the directrix and the focus.

So the vertex here is (4, 3)

Where h = 4 and k = 3

|p| is the distance between the directrix and the vertex (p is negative as it is over the vertex)

p = -2

The equation of the parabola is

(x - h)² = 4p (y - k)

Substituting the values

(x - 4)² = 4 (-2) (y - 3)

(x - 4)²  = -8 (y - 3)

Therefore, the quadratic function created is (x - 4)²  = -8 (y - 3).

Using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created?

Summary:

Using a directrix of y = 5 and a focus of (4, 1), the quadratic function created is (x - 4)²  = -8 (y - 3).