Find the equation of the parabola

Question

y = ax2 + bx + c
that passes through the points. To verify your result, use a graphing utility to plot the points and graph the parabola.
(0,1)(1,2)(2,1)

Answer 1

clearly the axis of symmetry is x=1
also, since the two y-values differ by 1, that gives us
y = -(x-1)^2 + 2 = -x^2 + 2x + 1

you can easily find several online graphing utilities. Two popular ones are
desmos.com
wolframalpha.com