If the equation given is y=2x^2 and the point given is (-1,2), how would you find the p value from the form (x-0)^2=4p(y-k)?

1 Answer
Aug 8, 2018

p=1/8

Explanation:

We can rearrange the formula:
x^2 = 4p(y-k) implies y = x^2/(4p) + k

Therefore, we know that the coefficient of x^2 is 2, hence
2 = 1/(4p) implies p = 1/8

We could also have just done this with the given point by plugging in the known values of x,y that work:
x^2 = 4p(y-k)
(-1)^2 = 4p(2-k) implies 1 = (8- 4k)p
Since we can see that the vertical shift is 0 (since the function also intercepts 0), we get k=0 i.e. 1 = 8p implies p = 1/8.