Quadratic Relations and Functions

Question

What is the equation of the parabola in vertex form given the directrix is y=1 and the vertex is (-1,2)

Answer 1

4p(y-k) = (x-h)^2

p=1, the graph is shifted one point

to the left, so h=-1 and 2 points up, k=2

4(y-2) = (x+1)^2

y-2 = (1/4)(x+1)^2

y = (1/4)(x+1)^2+2

Answer 2

Hi Mani!

So this is a parabola that opens up bc the directrix is below the vertex.

y = (1/4p)(x-h)²+ k where (h,k) is the vertex

So when you replace h and k you will get this:

y= (1/4p) (x+1)² +2

p is the distance from the vertex to the focus

directrix is -p from the vertex.

since the directrix y=1 is 1 unit below the vertex (-1,2) then we can say p=1

a=1/4(1)

a=1/4

y= 1/4(x+1)² +2