Find the quadratic polynomial whose graph passes through the points (0,0) (-1,1) and (1,1).
I used solved the linear system 0 = f(0) = $\displaystyle a_3 $ 1 = f(-1) = $\displaystyle a_2 - a_1 + a_0 $ 1 = f(1) = $\displaystyle a_2 + a_1 + a_0 $.
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 $\displaystyle y= ax^2+ bx+ c$ for some numbers, a, b, and c. When x= 0, y= 0 so $\displaystyle 0= a(0^2)+ b(0)+ c$ so c= 0. Then when x= -1, y= 1 so $\displaystyle 1= a(-1)^2+ b(-1)$ or $\displaystyle a- b= 1$. Finally, when x= 1, y= 1 so $\displaystyle 1= a(1)^2+ b(1)$ or a+ b= 1.
Solve the two equations a+ b= 1 and a- b= 1 for a and b.