Using a directrix of y = −2 and a focus of (2, 6), what quadratic function is created?
Answer:
\((x-2)^2= 16(y-2)\)
Step-by-step explanation:
Using a directrix of y = −2 and a focus of (2, 6). find the quadratic function
Vertex form of a parabola is \((x-h)^2= 4p(y-k)\)
where (h,k) is the vertex and p is the distance between the vertex and focus
Vertex lies in the middle of directrix and focus
Distance between directrix and focus is 6-(-2)= 8 divide by 2 is 4
now subtract 4 from y
when parabola opens up the x value remains the same
so vertex is (2, 6-4) becomes (2,2)
Vertex is (2,2)
Distance between focus and vertex is 4 that is our p
\((x-h)^2= 4p(y-k)\)
Plug in h=2 , k=2, p=4
\((x-2)^2= 4(4)(y-2)\)
\((x-2)^2= 16(y-2)\)