Answer:
[tex]y = - \frac{1}{24} (x + 5) + 1[/tex]
Explanation
The directrix y=7, is above the y-value of the focus. The parabola must will open downwards.
Such parabola has equation of the form,
[tex] {(x - h)}^{2} = - 4p(y - k)[/tex]
where (h,k) is the vertex.
The vertex is the midway from the focus to the directrix
The x-value of the vertex is x=-5 because it is on a vertical line that goes through (-5,-5).
The y-value of the vertex is
[tex]y = \frac{ 7 + - 5}{2} [/tex]
[tex]y = \frac{ 2}{2} = 1[/tex]
The equation of the parabola now becomes
[tex]{(x + 5)}^{2} = - 4p(y - 1)[/tex]
p is the distance from the focus to the vertex which is p=|7-1|=6
Substitute the value of p to get:
[tex]{(x + 5)}^{2} = - 4 \times 6(y - 1)[/tex]
[tex]{(x + 5)}^{2} = - 24(y - 1)[/tex]
We solve for y to get:
[tex]y = - \frac{1}{24} (x + 5) + 1[/tex]
Answer:
f(x) = −one twentyfourth (x + 5)2 + 1
Step-by-step explanation:
