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# 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).

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