Calculus
posted by George .
If you can helpme on this problem you are GOD.
If f(x) = ax^2 + bx + c, what can you say about the values of a, b, and c if:
(A) (1,1) is on the graph of f(x)?
(B) (1,1) is the vertex of the graph of f(x)?[Hint: The axis of symmetry is x = b/(2a).]
(c)The y intercept of the graph is (0,6)?
(D) Find a quadriatic function satisfying all three conditions.

from (A) we would know that 1 = a + b + c
from (b) we know 1 = b((2a)
or b = 2a
from (c) we know that at the yintercept x = 0
so 6 = 0 + 0 + c, so c=6
so back in the first equation
a+b+c = 1
a + (2a) + 6 = 1
a = 5
a + 5, then b = 10 and c=6
so f(x) = 5x^2  10x + 6