SOLUTION: I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!!! I would deeply appreciate it!! Find

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Question 195651This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!!! I would deeply appreciate it!!
Find an equation of the parabola having vertex (0,0) and directrix y=2. This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Keep in mind that the parabola form we'll use is

%28x-h%29%5E2=4p%28y-k%29 where "p" is the distance from the vertex to the focus.


It turns out that the distance from the directrix to the vertex is equal to the distance from the vertex to the focus. Since the distance from the directrix y = 2 to the vertex (0,0) is 2 units, this means that p=2


Also, since the vertex is (0,0), this means that h=0 and k=0


So all we need to do is plug these values in and isolate "y":


%28x-h%29%5E2=4p%28y-k%29 Start with the given equation.


%28x-0%29%5E2=4%282%29%28y-0%29 Plug in p=2, h=0 and k=0


x%5E2=4%282%29y Simplify


x%5E2=8y Multiply


%281%2F8%29x%5E2=y Multiply both sides by 1%2F8 to isolate "y".


y=%281%2F8%29x%5E2 Rearrange the terms.


Now because the parabola has the directrix above the vertex, this means that the parabola is opening down. So this means we need to attach a negative sign to the coefficient: y=-%281%2F8%29x%5E2



So the equation is y=-%281%2F8%29x%5E2