Will mark brainliest using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created? f(x) = 1/4(x − 4)^2 − 3 f(x) = 1/8(x + 4)^2 − 3 f(x) = −1/8(x − 4)^2 + 3 f(x) = −1/4(x + 4)^2 − 3

Step-by-step explanation:

The directrix given to us has equation,

and the focus is .  

This means that the axis of symmetry of the parabola is parallel to the y-axis and has equation , because it must go through the focus.

This axis of symmetry of the parabola will meet the directrix at .

The vertex of this parabola is the midpoint of the point of intersection of the axis of symmetry and the focus.

Thus,

.

The equation is given by .

.

is the distance between the vertex and the focus, which is 2.

This implies that,

or

But the position of the directrix and the vertex implies that  the parabola opens downwards.

.

The equation of the parabola now becomes;

.

We solve for y to obtain,

or