SOLUTION: The graph of a quadratic function opens downward with vertex at (3, 9). If the parabola passes through the origin, find the equation of the quadratic function.

Question 1139595: The graph of a quadratic function opens downward with vertex at (3, 9). If the parabola passes through the origin, find the equation of the quadratic function.
Answer by ikleyn(52793) (Show Source): You can put this solution on YOUR website!
.

Your quadratic function is


    f(x) =  + 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.


     + 9 = 0

     + 9 = 0

    9a = -9

    a =  = 1.


ANSWER.  The equation of the quadratic function is  f(x) =  + 9.

Solved.

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