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}}}.
<pre>
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".

{{{"f(x)"=a(x-2)^2+8}}}.

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

{{{y=a(x-2)^2+8}}}.

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

{{{6=a*(8-2)^2+8}}}

{{{6=a*(6)^2+8}}}

{{{6=a*(36)+8}}}

{{{6=36a+8}}}

{{{-2=36a}}}

{{{(-2)/36=a}}}

{{{-1/18=a}}}

Now to check let's draw the graph of

{{{"f(x)"=expr(-1/18)(x-2)^2+8}}}.


{{{drawing(800,400,-14,18,-6,10,

circle(2,8,.15), circle(8,6,.15),
locate(1,9,"(2,8)vertex"), locate(8.5,6.5,"(8,6)passes_thru"),

graph(800,400,-14,18,-6,10,(-1/18)(x-2)^2+8)  )}}}

Edwin</pre>