Respuesta :

The answer is A. If you plug the focus and the directrix into a graph and find the focal length and plug it into the 1/4(a) equation you get 1/20 then plug in the h and the k from the vertex and its negative because the directrix is above the focus and vertex.



A. F(x) = -1/20 (x-4)^2+5

Answer:

The correct option is 1.

Step-by-step explanation:

The general equation of a parabola is

[tex](x-h)^2=4p(y-k)[/tex]

Where, (h,k+p) is focus and y=k-p is directrix .

The focus of parabola is (4,0).

[tex](h,k+p)=(4,0)[/tex]

[tex]h=4[/tex]

[tex]k+p=0[/tex]           .... (1)

The directrix of parabola is  y=10.

[tex]k-p=10[/tex]             .... (2).

Add equation (1) and (2).

[tex]2k=10[/tex]

[tex]k=5[/tex]

[tex]p=-5[/tex]

The equation of the parabola is

[tex](x-4)^2=4(-5)(y-5)[/tex]

[tex](x-4)^2=-20(y-5)[/tex]

[tex]-\frac{1}{20}(x-4)^2=(y-5)[/tex]

[tex]-\frac{1}{20}(x-4)^2+5=y[/tex]

[tex]f(x)=-\frac{1}{20}(x-4)^2+5[/tex]

Therefore option 1 is correct.

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