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.

Algebra ->  Graphs -> 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.      Log On


   

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(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Your quadratic function is


    f(x) = a%2A%28x-3%29%5E2 + 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%2A%280-3%29%5E2 + 9 = 0

    a%2A3%5E2 + 9 = 0

    9a = -9

    a = -9%2F9 = 1.


ANSWER.  The equation of the quadratic function is  f(x) = -%28x-3%29%5E2 + 9.

Solved.