Question

Using a directrix of y = -2 and a focus of (2, 6), what quadratic function is created?

Answer 1

f(x) = -1/8(x - 2)2 - 2

f(x) = 1/16(x - 2)2 + 2

f(x) = 1/8(x - 2)2 - 2

f(x) = - 1/16(x + 2)2 - 2

Answer 2

we don't need to do much work since you have choices
do you know what this looks like?

Answer 3

ok good and not really /:

Answer 4

i will graph the focus and directrix

Answer 5

the vertex is half way between the focus and the directrix, so it is at \((2,2)\)

Answer 6

ok i follow you

Answer 7

then the equation is has to be either
f(x) = 1/16(x - 2)2 + 2 or
f(x) = 1/8(x - 2)2 - 2 because it opens up the distance between the vertex and the directrix is \(p=4\) so \(4p=16\) pick

Answer 8

pick
\[f(x)=\frac{1}{16}(x-2)^2+2\]

Answer 9

here is the check
http://www.wolframalpha.com/input/?i=parabola+y%3D1%2F16%28x+-+2%29^2+%2B+2

Answer 10

ok thanks for all your help (:

Answer 11

In f(x) = a(x-h)^2 + k, (h,k) is the vertex.
Here the vertex is (2,2) and so the choice is f(x) = 1/16(x-2)^2 + 2

Answer 12

yw

Answer 13

ok thank you to @aum for the effort! (: