SOLUTION: Hi, can I have some help finding a function whose graph is a parabola with vertex (6, -4) and that passes through the point (1, 8)? Thanks

Algebra ->  Equations -> SOLUTION: Hi, can I have some help finding a function whose graph is a parabola with vertex (6, -4) and that passes through the point (1, 8)? Thanks      Log On


   

Question 127806: Hi, can I have some help finding a function whose graph is a parabola with vertex (6, -4) and that passes through the point (1, 8)?
Thanks
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The equation of a parabola with vertex at (h,k), and directrix at y=k-p is %28x-h%29%5E2=4p%28y-k%29.

The vertex is given, so we can write:

%28x-6%29%5E2=4p%28y%2B4%29

Now we have to calculate p given that the parabola passes through (1,8).

%281-6%29%5E2=4p%288%2B4%29

25=48p

p=25%2F48

Now we have:
%28x-6%29%5E2=4%2825%2F48%29%28y%2B4%29

x%5E2-12x%2B36=%2825%2F12%29%28y%2B4%29

%2812%2F25%29%28x%5E2-12x%2B36%29=y%2B4

%2812x%5E2-144x%2B432-100%29%2F25=y

So: f%28x%29=y=%2812x%5E2-144x%2B332%29%2F25