Question 420107
(0,0) ==> {{{a*0^2 + b*0 + c = 0}}} ==> c = 0.

(4,7) and (-4, 9) ==> 16a + 4b = 7, and 16a - 4b = 9 by direct substitution.

Adding corresponding sides, we get 

32a = 16, or a = 1/2.

Substituting this a value into 16a + 4b = 7, we get b = -1/4.

Then ab = -1/8.