what are the vertex focus and directrix of the parabole with the giving equation y = 1/12 (x-4)^2-5

Question

campbell_st · Answer

the standard vertex form is 

$$y = \frac{1}{4a}(x -h)^2 + k$$

(h, k) is the vertex.... 

that's the 1st piece of information.... so match the equation to this to find h and k.

the value a is called the focal length....(distance from the focus to the vertex)

so compare 

$$\frac{1}{4a} = \frac{1}{12}$$

and find the value of a. 

the focus will then be located at 

(h, k+a)

the directrix equation is 

y = k - a

hope it helps