Find quadratic function y=ax^2+c using points....???

1).(0,2) and (3,5)


2.) (2,5/2) and (0, -1/2)

Find quadratic function y=ax^2+c using points....???
1.


Putting x = 0, y = 2 in y = ax^2 + c:


a0^2 + c = 2 ...(1)





Puttijng x = 3, y = 5 in y = ax^2 + c:


a3^2 + c = 5 ...(2)





From (1), c = 2.


Substituting for c in (2):


9a + 2 = 5


a = 3 / 9 = 1/3.





The function is:


y = (1/3)x^2 + 2.





2.


Using the same technique:


5/2 = 4a + c ...(3)


-1/2 = c





From (3):


5/2 = 4a - 1/2


6/2 = 4a


3 = 4a


a = 3/4.





The function is:


y = (3/4)x^2 - 1/2.