SOLUTION: If a quadratic function has its vertex at point (2,8) and the function passes through point (8,6), what is a,h, and k when written in vertex form if the function is f(x)=a(x-h)^2+k

Algebra ->  College  -> Linear Algebra -> SOLUTION: If a quadratic function has its vertex at point (2,8) and the function passes through point (8,6), what is a,h, and k when written in vertex form if the function is f(x)=a(x-h)^2+k      Log On


   



Question 365215: If a quadratic function has its vertex at point (2,8) and the function passes through point (8,6), what is a,h, and k when written in vertex form if the function is f(x)=a(x-h)^2+k.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
If a quadratic function has its vertex at point (2,8) and the function passes through point (8,6), what is a,h, and k when written in vertex form if the function is %22f%28x%29%22=a%28x-h%29%5E2%2Bk.
Since it has vertex (h,k) = (2,8), 

h = 2 and k = 8.  That's 2/3rds of what you asked for!  All you

need is "a".

%22f%28x%29%22=a%28x-2%29%5E2%2B8.

Since f(x) is the same as y, let's write it:

y=a%28x-2%29%5E2%2B8.

Since it goes through (8,6) we substitute 8 for x, and 6 for y

6=a%2A%288-2%29%5E2%2B8

6=a%2A%286%29%5E2%2B8

6=a%2A%2836%29%2B8

6=36a%2B8

-2=36a

%28-2%29%2F36=a

-1%2F18=a

Now to check let's draw the graph of

%22f%28x%29%22=expr%28-1%2F18%29%28x-2%29%5E2%2B8.




Edwin