Question

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.

Answer 1

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 y-intercept 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