How do you find the quadratic function y = a x 2 + b x + c whose graph passes through the given points. (1, 2),(0,1 ), (2,1)?

Answer 1

if the graph of this functions passes through those points, that means those points satisfy the function.if we plug in those points into the function, we get the following equations

a+b+c=2

c=1

4a+2b+c=1

since c=1 and if we plug that in two equations above, we get the following system of linear equations

a+b=1

4a+2b=0

when we solve these two equations, we get a=-1,b=2 and c=1.when we put all these numbers back into the original functions, we get f(x)=-x²+2x+1