Expert: Sherman D. - 3/25/2004

Question
given the focus (3,8) and y=4 as the directrix how do you write the equation for the parabola and how do you graph it?  

Answer
focus is (h, k + 1/(4a))

directrix is y = k - 1/(4a)

4 = k - 1/4a

k + 1/(4a) = 8
k = 8 - (1/(4a))

4 = (8 - (1/4a)) - (1/(4a))
4 = 8 - (1/4a) - (1/(4a))
4 = 8 - 2(1/(4a))
4 = 8 - (2/(4a))
4 = 8 - (1/(2a))
-4 = -(1/(2a))
-8a = -1
a = (1/8)

h = 3
a = (1/8)
y = 4

h = -b/(2a)
k = ax² + bx + c

3 = -b/(2(1/8))
3 = -b/(2/8)
3 = -b/(1/4)
(3/4) = -b
b = (-3/4)

k = (1/8)x^2 - (3/4)x + c

k = -(b² - 4ac)/(4a)
4 = -((-3/4)^2 - 4((1/8)c))/(4(1/8))
4 = -((9/16) - (4/8)c)/(1/2)
4 = -((9/16) - (1/2)c)/(1/2)
2 = -(9/16) + (1/2)c
(41/16) = (1/2)c
c = (41/8)

y = (1/8)x^2 - (3/4)x + (41/8)

Using http://mcraefamily.com/MathHelp/factoring4.htm

that is what i got, and i have no idea for sure if it is correct, since i haven't done problems like those in a long time.