Answer:
Vertex - (4,-5)
Focus (4,2)
Directrix y=-12
Step-by-step explanation:
The equation [tex]y=\dfrac{1}{28}(x-4)^2-5[/tex] of the parabola shows that its vertex is at point (4,-5). Multiply the equation by 28:
[tex]28y=(x-4)^2-140\Rightarrow (x-4)^2=28y+140,\\ \\(x-4)^2=28(y+5).[/tex]
The parameter p of the parabola is
[tex]2p=28\Rightarrow p=14.[/tex]
The coordinates of the focus will be
[tex]\left(4,-5+\dfrac{p}{2}\right)=\left(4,-5+\dfrac{14}{2}\right)=\left(4,2\right).[/tex]
The directrix has the equation
[tex]y=-5-\dfrac{p}{2}\Rightarrow y=-5-7,\ y=-12.[/tex]
