SOLUTION: find a formula ( in the form f(x)=ax2+bx+c) for aquadratic function with roots 1/2 and 6, and where the point (2,-56) is on the graph of the function

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: find a formula ( in the form f(x)=ax2+bx+c) for aquadratic function with roots 1/2 and 6, and where the point (2,-56) is on the graph of the function      Log On


   

Question 576132: find a formula ( in the form f(x)=ax2+bx+c) for aquadratic function with roots 1/2 and 6, and where the point (2,-56) is on the graph of the function
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is actually 3 points,
( 1/2,0), (6,0), and(2,-56)
I can write:
(1) +0+=+a%2A%281%2F2%29%5E2+%2B+b%2A%281%2F2%29+%2B+c+
(2) +0+=+a%2A6%5E2+%2B+b%2A6+%2B+c+
(3) +-56+=+a%2A2%5E2+%2B+b%2A2+%2B+c+
--------------------------
(1) +%281%2F4%29%2Aa+%2B+%281%2F2%29%2Ab+%2B+c+=+0+
(1) +a+%2B+2b+%2B+4c+=+0+
(2) +36a+%2B+6b+%2B+c+=+0+
(3) ++4a+%2B+2b+%2B+c+-+56+
Subtract (1) from (3)
This is 3 equations and 3 unknowns, so
you can solve for a,b, and c to get
+f%28x%29+=+ax%5E2+%2B+bx+%2B+c+