Question 1139595
.
<pre>
Your quadratic function is


    f(x) = {{{a*(x-3)^2}}} + 9,


according to the condition,  where "a" is negative coefficient.


To find "a", use the second part of the condition: the parabola passes through the origin.


It means that f(0) = 0, i.e.


    {{{a*(0-3)^2}}} + 9 = 0

    {{{a*3^2}}} + 9 = 0

    9a = -9

    a = {{{-9/9}}} = 1.


<U>ANSWER</U>.  The equation of the quadratic function is  f(x) = {{{-(x-3)^2}}} + 9.
</pre>

Solved.