Find the quadratic function y=ax^ (2) + c with a graph that includes (0,1/2) (-3,73/2).

A. y=-4x^2-1/2

B. y=4x^2+1/2

C. 4x^2-1/2

D. none of these

The answer is B. The way you find it is through substitution. First use the coordinate (0, 1/2) in y = ax^2 + c to solve for c: 1/2=a (0) ^2 + c--> 1/2=c. Now use that c value in the same y = ax^2 + c equation with the other coordinate to solve for a: 73/2 = a (-3) ^2 + 1/2. Subtract 1/2 from both sides to get 72/2=9a. 72/2 is 36. So 36 = 9a ... a = 4. Now fill in your a and your c to get y = 4x^2 + 1/2