I used solved the linear system 0 = f(0) = 1 = f(-1) = 1 = f(1) = .
Then i looked at the question, the points and slapped my self on my forehead and erased all my work to save embarrassment.
Any "quadratic polynomial" can be written in the form for some numbers, a, b, and c. When x= 0, y= 0 so so c= 0. Then when x= -1, y= 1 so or . Finally, when x= 1, y= 1 so or a+ b= 1.
Solve the two equations a+ b= 1 and a- b= 1 for a and b.