SOLUTION: Determine the quadratic function,F(x)=a^2+bx+c , whose vertex is (3, 7) and passes through the point (5, -9).

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Determine the quadratic function,F(x)=a^2+bx+c , whose vertex is (3, 7) and passes through the point (5, -9).      Log On


   

Question 542429: Determine the quadratic function,F(x)=a^2+bx+c , whose vertex is (3, 7) and passes through the point (5, -9).
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A quadratic functions whose vertex is (3,7) can be written (in vertex form) as
f%28x%29=a%28x-3%29%5E2%2B7
If it passes through (5,-9), f%285%29=-9, so
a%285-3%29%5E2%2B7=-9 --> 4a%2B7=-9 --> 4a=-16 --> a=-4
f%28x%29=-4%28x-3%29%5E2%2B7 <---> f%28x%29=-4x%5E2%2B24x-29